{"id":784,"date":"2024-03-21T13:13:02","date_gmt":"2024-03-21T04:13:02","guid":{"rendered":"https:\/\/y-page.y.kumamoto-nct.ac.jp\/wp\/Math_23\/?p=784"},"modified":"2024-06-03T09:11:14","modified_gmt":"2024-06-03T00:11:14","slug":"top-math2-1q-4h-1","status":"publish","type":"post","link":"https:\/\/y-page.y.kumamoto-nct.ac.jp\/wp\/Math_23\/?p=784","title":{"rendered":"\u6570\u5b66II_1Q4H_1"},"content":{"rendered":"\n\n\n\n\n
\u00a0<\/span><\/td>\n\u00a0<\/span><\/td>\n\u00a0<\/span><\/td>\n\u00a0<\/span><\/td>\nNext<\/span><\/a><\/td>\n<\/tr>\n
\u00a0<\/span><\/td>\n\u00a0<\/span><\/td>\n\u00a0<\/span><\/td>\n\u00a0<\/td>\n\u518d\u751f\u30ea\u30b9\u30c8<\/span><\/a><\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n\n\n\n\n\n\n\n
\u30c6\u30ad\u30b9\u30c8<\/span><\/td>\n\u6f14\u7fd2<\/span><\/td>\n\u6f14\u7fd2\u89e3\u7b54<\/span><\/td>\n\u8ab2\u984c<\/span><\/td>\n\u89e3\u8aac<\/span><\/td>\n<\/tr>\n
1Q4H_1<\/a><\/td>\n1Q4H_E1<\/a><\/td>\n1Q4H_ES1<\/a><\/td>\n1Q4H_K1<\/a><\/td>\n1Q4H_V1<\/span><\/a><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n\n\n\n
<\/span> \u521d\u9805$a$ \u516c\u5dee$d$ \u306e\u7b49\u5dee\u6570\u5217\u306e\u4e00\u822c\u9805 $a_n=?$ <\/div>
$a_n=$$a$<\/span>$+(n-1)$$d$<\/span>$=dn+(a-d)$ <\/div><\/div>
<\/span>Targets<\/div>
1. \u6f38\u5316\u5f0f<\/span>\u3092\u81ea\u5206\u3067\u4f5c\u6210\u3057\u6700\u521d\u306e\uff15\u9805\u3092\u6c42\u3081\u308b\u3053\u3068\u304c\u3067\u304d\u308b
2. \u7b49\u5dee\u6570\u5217<\/span>\u306e\u4f8b\u3092\u4f5c\u308b\u3053\u3068\u304c\u3067\u304d\u308b
3. \uff12\u3067\u81ea\u4f5c\u3057\u305f\u4f8b\u304b\u3089\u4e00\u822c\u9805<\/span>\u3092\u6c42\u3081\u308b\u3053\u3068\u304c\u3067\u304d\u308b
4. \uff12\u3067\u81ea\u4f5c\u3057\u305f\u4f8b\u304b\u3089\u7b2c100\u9805<\/span>\u3092\u6c42\u3081\u308b\u3053\u3068\u304c\u3067\u304d\u308b
5. \u7b49\u5dee\u6570\u5217\u306e\u7570\u306a\u308b2\u9805\u3092\u4e0e\u3048\u3066\u3001\u521d\u9805<\/span>\u3068\u516c\u5dee<\/span>\u3092\u6c42\u3081\u308b\u3053\u3068\u304c\u3067\u304d\u308b <\/div><\/div> <\/div>\n
\n\n\n\n\n\n
1Q4H_2<\/a><\/td>\n1Q4H_E2<\/a><\/td>\n1Q4H_ES2<\/a><\/td>\n1Q4H_K2<\/a><\/td>\n1Q4H_V2<\/a><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n\n\n
<\/span> \u521d\u9805$a$ \u516c\u6bd4$r$ \u306e\u7b49\u6bd4\u6570\u5217\u306e\u4e00\u822c\u9805 $a_n=?$ <\/div>
$a_n=$$a$<\/span>$\\cdot$$r$<\/span>$^{n-1}$<\/div><\/div>
<\/span>Targets<\/div>
1. \u7b49\u6bd4\u6570\u5217<\/span>\u306e\u4f8b\u3092\u4f5c\u308b\u3053\u3068\u304c\u3067\u304d\u308b
2. \uff11\u3067\u81ea\u4f5c\u3057\u305f\u4f8b\u304b\u3089\u4e00\u822c\u9805<\/span>\u3092\u6c42\u3081\u308b\u3053\u3068\u304c\u3067\u304d\u308b
3. \uff11\u3067\u81ea\u4f5c\u3057\u305f\u4f8b\u304b\u3089\u7b2c8\u9805<\/span>\u3092\u6c42\u3081\u308b\u3053\u3068\u304c\u3067\u304d\u308b
4. \u7b49\u6bd4\u6570\u5217\u306e\u7570\u306a\u308b2\u9805\u3092\u4e0e\u3048\u3066\u3001\u521d\u9805<\/span>\u3068\u516c\u6bd4<\/span>\u3092\u6c42\u3081\u308b\u3053\u3068\u304c\u3067\u304d\u308b
5. \u6570\u5217\u306e\u4e00\u822c\u9805\u3092\u4e0e\u3048\u3066\u7b2c\uff13\u9805\u304b\u3089\u7b2c\uff18\u9805\u307e\u3067\u306e\u548c\u3092
\u3000\u548c\u306e\u8a18\u53f7$\\Sigma$<\/span>\u3092\u7528\u3044\u3066\u8868\u793a\u3067\u304d\u308b <\/div><\/div> <\/div>\n
\n\n\n\n\n\n\n
1Q4H_3<\/a><\/td>\n1Q4H_E3<\/a><\/td>\n1Q4H_ES3<\/a><\/td>\n1Q4H_K3<\/a><\/td>\n1Q4H_V3<\/a><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n\n\n
<\/span> \u521d\u9805$a$ \u516c\u5dee$d$ \u306e\u7b49\u5dee\u6570\u5217\u306e$n$\u9805\u307e\u3067\u306e\u548c$S_n=?$\u3001\u03a3$k=?$\u3001\u03a3$k^2=?$\u3001\u03a3$k^3=?$<\/div>
$S_n=\\frac{1}{2}n(a+a_n)=\\frac{1}{2}n \\{$2$a$<\/span>$+(n-1)$$d$<\/span>$\\}=\\frac{1}{2}n(dn+2a-d)$
$\\displaystyle{\\sum_{k=1}^{n}k}=\\frac{1}{2}n(n+1)$\u3001$\\; \\displaystyle{\\sum_{k=1}^{n}k^2}=\\frac{1}{6}n(n+1)(2n+1)$
$\\displaystyle{\\sum_{k=1}^{n}k^3}=\\frac{1}{4}n^2(n+1)^2$
\u8a3c\u660e\uff1a1Q4H_V3_pf<\/span><\/a><\/div><\/div>
<\/span>Targets<\/div>
1. \u7b49\u5dee\u6570\u5217<\/span>\u306e\u4f8b\u3092\u4e0e\u3048\u3066\u3001\u521d\u9805\u304b\u3089$n$\u9805\u307e\u3067\u306e\u548c<\/span>\u3092\u6c42\u3081\u308b\u3053\u3068\u304c\u3067\u304d\u308b
2. \uff11\u3067\u81ea\u4f5c\u3057\u305f\u4f8b\u3092\u7528\u3044\u3066\uff13\u9805\u304b\u3089100\u9805\u307e\u3067\u306e\u548c<\/span>\u3092\u6c42\u3081\u308b\u3053\u3068\u304c\u3067\u304d\u308b\u3002
3. \u4e00\u822c\u9805\u304c\uff12\u6b21\u5f0f<\/span>\u3067\u4e0e\u3048\u3089\u308c\u305f\u6570\u5217\u306e\u521d\u9805\u304b\u3089$n$\u9805\u307e\u3067\u306e\u548c\u3092
\u3000\u548c\u306e\u8a18\u53f7$\\Sigma$<\/span>\u3092\u7528\u3044\u3066\u6c42\u3081\u308b\u3053\u3068\u304c\u3067\u304d\u308b
\u2190 $\\displaystyle{\\sum_{k=1}^{n}(ak+b)}=?$<\/span>
\u2190$\\displaystyle{\\sum_{k=1}^{n}k^2}=?$<\/span><\/div><\/div> <\/div>\n
\n\n\n\n\n\n
1Q4H_4<\/a><\/td>\n1Q4H_E4<\/a><\/td>\n1Q4H_ES4<\/a><\/td>\n1Q4H_K4<\/a><\/td>\n1Q4H_V4<\/a><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n\n\n
<\/span> \u521d\u9805$a$ \u516c\u6bd4$r$ \u306e\u7b49\u6bd4\u6570\u5217\u306e$n$\u9805\u307e\u3067\u306e\u548c$S_n=?$\u3001\u03a3$1\/a_k$$a_k$$_+$$_1=?$<\/div>
$S_n=$$a$<\/span>$\\cdot \\displaystyle{\\frac{1-r^n}{1-r}}=$$a$<\/span>$\\cdot \\displaystyle{\\frac{r^n-1}{r-1}}$ if $r\\neq1$\u3001 $S_n=$$a$<\/span>$n$ if $r=1$
$\\displaystyle{\\sum_{k=1}^{n} \\frac{1}{a_ka_{k+1}}}=\\frac{1}{d}\\Big( \\frac{1}{a_1}-\\frac{1}{a_{n+1}} \\Big)$ if $a_{k+1}-a_k=d$
\u8a3c\u660e\uff1a1Q4H_V4_pf<\/span><\/a><\/div><\/div>
<\/span>Targets<\/div>
1. \u7b49\u6bd4\u6570\u5217<\/span>\u306e\u4f8b\u3092\u4e0e\u3048\u3066\u3001\u521d\u9805\u304b\u3089n\u9805\u307e\u3067\u306e\u548c<\/span>\u3092\u6c42\u3081\u308b\u3053\u3068\u304c\u3067\u304d\u308b
2. \uff11\u3067\u81ea\u4f5c\u3057\u305f\u4f8b\u3067\u3001\u521d\u9805\u304b\u3089\uff18\u9805\u307e\u3067\u306e\u548c<\/span>\u3092\u6c42\u3081\u308b\u3053\u3068\u304c\u3067\u304d\u308b
3. \u4e00\u822c\u9805\u304c\u7b49\u5dee\u6570\u5217\u306ek\u9805\u3068k+1\u9805\u306e\u7a4d\u306e\u9006\u6570\u306e\u548c<\/span>\u3092\u6c42\u3081\u308b\u3053\u3068\u304c\u3067\u304d\u308b
\u3000\u2190\u90e8\u5206\u5206\u6570\u5206\u89e3<\/span><\/div><\/div> <\/div>\n
\n\n\n\n\n\n
1Q4H_5<\/a><\/td>\n1Q4H_E5<\/a><\/td>\n1Q4H_ES5<\/a><\/td>\n1Q4H_K5<\/a><\/td>\n1Q4H_V5<\/a><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n\n\n\n
<\/span> $b_k=a_k$$_+$$_1-a_k$ \u2192 $a_n=?$ \u3001$a_n$$_+$$_1=ra_n+b$ ($r$\u2260$1$) \u2192 $a_n=?$<\/div>
$b_k=a_{k+1}-a_k \\rightarrow a_n=a_1+\\displaystyle{\\sum_{k=1}^{n-1}b_k}$
$a_{n+1}=ra_n+b$ ($r \\neq 1$) $\\rightarrow a_n-\\lambda=(a_1-\\lambda)\\cdot r^{n-1}\u3000\\; \\big( \\lambda =r \\lambda +b)$
\u8a3c\u660e\uff1a1Q4H_V5_pf<\/span><\/a><\/div><\/div>
<\/span>Targets<\/div>
1. \u968e\u5dee\u6570\u5217<\/span>\u304b\u3089\u5143\u306e\u6570\u5217\u306e\u4e00\u822c\u9805<\/span>\u3092\u6c42\u3081\u308b\u3053\u3068\u304c\u3067\u304d\u308b
2. $a_{n+1}=a_n+b_n$<\/span> \u578b\u306e\u6f38\u5316\u5f0f\u306e\u4f8b\u3092\u4f5c\u308a\u89e3\u304f\u3053\u3068\u304c\u3067\u304d\u308b
3. $a_{n+1}=ra_n+b$<\/span> ($r \\neq 1$) \u578b\u306e\u6f38\u5316\u5f0f\u306e\u4f8b\u3092\u4f5c\u308a\u89e3\u304f\u3053\u3068\u304c\u3067\u304d\u308b <\/div><\/div> <\/div>\n
\n\n\n\n\n\n\n
1Q4H_6<\/a><\/td>\n1Q4H_E6<\/a><\/td>\n1Q4H_ES6<\/a><\/td>\n1Q4H_K6<\/a><\/td>\n1Q4H_V6<\/a><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n\n\n
<\/span> \u6570\u5b66\u7684\u5e30\u7d0d\u6cd5\u306e\uff13\u30b9\u30c6\u30c3\u30d7\u306f\uff1f<\/div>
\uff11\uff0e$n=1$\u306e\u3068\u304d\u3001\u6210\u308a\u7acb\u3064\u3053\u3068\u3092\u793a\u3059
\uff12\uff0e$n=k$\u306e\u6642\u6210\u308a\u7acb\u3064\u3068\u4eee\u5b9a\u3057\u3066\u3001$n=k+1$\u306e\u3068\u304d\u6210\u308a\u7acb\u3064\u3053\u3068\u3092\u5c0e\u304f
\uff13\uff0e\u30b9\u30c6\u30c3\u30d71,2\u3088\u308a\u3059\u3079\u3066\u306e\u81ea\u7136\u6570$n$\u306b\u5bfe\u3057\u3066\u4e3b\u5f35\u304c\u6210\u308a\u7acb\u3064<\/div><\/div>
<\/span>Targets<\/div>
1. \u30c6\u30ad\u30b9\u30c8\u3092\u8aad\u307f\u3001\u6570\u5b66\u7684\u5e30\u7d0d\u6cd5\u306e\uff13\u30b9\u30c6\u30c3\u30d7<\/span>\u3092\u66f8\u304f\u3053\u3068\u304c\u3067\u304d\u308b
2. \u6570\u5b66\u7684\u5e30\u7d0d\u6cd5<\/span>\u3067\u8a3c\u660e\u3067\u304d\u308b\u554f\u984c\u3092\u4e00\u3064\u898b\u3064\u3051\u3066\u3001\u8a3c\u660e\u3092\u66f8\u304f\u3053\u3068\u304c\u3067\u304d\u308b <\/div><\/div> <\/div>\n
\n\n\n\n\n\n
\u00a0<\/span><\/td>\n\u00a0<\/span><\/td>\n\u00a0<\/span><\/td>\n\u00a0<\/span><\/td>\nNext<\/span><\/a><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n","protected":false},"excerpt":{"rendered":"

\u00a0 \u00a0 \u00a0 \u00a0 Next \u00a0 \u00a0 \u00a0 \u00a0 \u518d\u751f\u30ea\u30b9\u30c8 \u30c6\u30ad\u30b9\u30c8 \u6f14\u7fd2 \u6f14\u7fd2\u89e3\u7b54 \u8ab2\u984c \u89e3\u8aac 1Q4H_1 1Q4H_E1 1Q4H_ES1 1Q4H_K1 1Q4H_V1 1Q4H_2 1Q4H_E2 1Q4H_ES2 […]<\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[42,14,4,7,32],"tags":[],"class_list":["post-784","post","type-post","status-publish","format-standard","hentry","category-si","category-top","category-math2","category-math2-1q","category-math2-1q4h-1"],"_links":{"self":[{"href":"https:\/\/y-page.y.kumamoto-nct.ac.jp\/wp\/Math_23\/index.php?rest_route=\/wp\/v2\/posts\/784","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/y-page.y.kumamoto-nct.ac.jp\/wp\/Math_23\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/y-page.y.kumamoto-nct.ac.jp\/wp\/Math_23\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/y-page.y.kumamoto-nct.ac.jp\/wp\/Math_23\/index.php?rest_route=\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/y-page.y.kumamoto-nct.ac.jp\/wp\/Math_23\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=784"}],"version-history":[{"count":17,"href":"https:\/\/y-page.y.kumamoto-nct.ac.jp\/wp\/Math_23\/index.php?rest_route=\/wp\/v2\/posts\/784\/revisions"}],"predecessor-version":[{"id":1873,"href":"https:\/\/y-page.y.kumamoto-nct.ac.jp\/wp\/Math_23\/index.php?rest_route=\/wp\/v2\/posts\/784\/revisions\/1873"}],"wp:attachment":[{"href":"https:\/\/y-page.y.kumamoto-nct.ac.jp\/wp\/Math_23\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=784"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/y-page.y.kumamoto-nct.ac.jp\/wp\/Math_23\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=784"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/y-page.y.kumamoto-nct.ac.jp\/wp\/Math_23\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=784"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}