\uff081\uff09\u901a\u9879\u516c\u5f0f<\/p>\n
$$
\na_n=a_1+(n-1)d
\n$$<\/p>\n
\uff082\uff09\u524dn\u9879\u548c\u516c\u5f0f<\/p>\n
$$
\nS_n=\\frac{(a_1+a_n)n}{2}
\n$$<\/p>\n
\uff083\uff09\u5e38\u7528\u6027\u8d28<\/p>\n
\u2460 \u82e5$m+n=p+q \\, (m,n,p,q \\in N_+)$\uff0c\u5219$a_m+a_n=a_p+a_q$\uff1b \uff081\uff09\u901a\u9879\u516c\u5f0f<\/p>\n $$ \uff082\uff09\u524dn\u9879\u548c\u516c\u5f0f<\/p>\n $$ \uff083\uff09\u5e38\u7528\u6027\u8d28<\/p>\n \u2460 \u82e5$m+n=p+q \\, (m,n,p,q \\in N_+)$\uff0c\u5219$a_m\u00b7a_n=a_p\u00b7a_q$\uff1b \u2460 \u5bf9\u79f0\u6027 $a > b \\Rightarrow b < a$ \u5e38\u7528\u65b9\u6cd5\u6709\uff1a\u6bd4\u8f83\u6cd5\uff08\u4f5c\u5dee\uff0c\u4f5c\u5546\u6cd5\uff09\u3001\u7efc\u5408\u6cd5\u3001\u5206\u6790\u6cd5\uff1b \u6570\u5217 \u7b49\u5dee\u6570\u5217 \uff081\uff09\u901a\u9879\u516c\u5f0f $$ a_n=a_1+(n-1)d $$ \uff082\uff09\u524dn\u9879\u548c\u516c\u5f0f $$ S_n=\\ […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[509],"tags":[],"class_list":["post-2121","post","type-post","status-publish","format-standard","hentry","category-mathematics-fundamentals"],"_links":{"self":[{"href":"https:\/\/www.appblog.cn\/index.php\/wp-json\/wp\/v2\/posts\/2121","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.appblog.cn\/index.php\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.appblog.cn\/index.php\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.appblog.cn\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.appblog.cn\/index.php\/wp-json\/wp\/v2\/comments?post=2121"}],"version-history":[{"count":0,"href":"https:\/\/www.appblog.cn\/index.php\/wp-json\/wp\/v2\/posts\/2121\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.appblog.cn\/index.php\/wp-json\/wp\/v2\/media?parent=2121"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.appblog.cn\/index.php\/wp-json\/wp\/v2\/categories?post=2121"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.appblog.cn\/index.php\/wp-json\/wp\/v2\/tags?post=2121"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}
\n\u2461 \u4e0b\u6807\u4e3a\u7b49\u5dee\u6570\u5217\u7684\u9879$(ak,a<\/em>{k+m},a_{k+2m},\u00b7\u00b7\u00b7)$\uff0c\u4ecd\u7ec4\u6210\u7b49\u5dee\u6570\u5217\uff1b
\n\u2462 \u6570\u5217$\\{\\lambda a_n+b\\}$ ($\\lambda,b$\u4e3a\u5e38\u6570)\u4ecd\u4e3a\u7b49\u5dee\u6570\u5217\uff1b
\n\u2463 \u82e5$\\{a_n\\}$\u3001$\\{b_n\\}$\u662f\u7b49\u5dee\u6570\u5217\uff0c\u5219$\\{ka_n\\}$\u3001$\\{ka_n+pbn\\}$($k$\u3001$p$\u662f\u975e\u96f6\u5e38\u6570)\u3001$\\{a<\/em>{p+nq}\\}$ $(p,q \\in N^*)\u00b7\u00b7\u00b7$ \u4e5f\u662f\u7b49\u5dee\u6570\u5217\uff1b
\n\u2464 \u5355\u8c03\u6027\uff1a$\\{a_n\\}$\u7684\u516c\u5dee\u4e3a$d$\uff0c\u5219\uff1a
\n1) $d>0 \\Leftrightarrow \\{a_n\\}$\u4e3a\u9012\u589e\u6570\u5217\uff1b
\n2) $d<0 \\Leftrightarrow \\{a_n\\}$\u4e3a\u9012\u51cf\u6570\u5217\uff1b
\n3) $d=0 \\Leftrightarrow \\{a_n\\}$\u4e3a\u5e38\u6570\u5217\uff1b
\n\u2465 \u82e5\u6570\u5217$\\{a_n\\}$\u4e3a\u7b49\u5dee\u6570\u5217$\\Leftrightarrow a_n=pn+q$ ($p,q$\u662f\u5e38\u6570)
\n\u2466 \u82e5\u7b49\u5dee\u6570\u5217$\\{a_n\\}$\u7684\u524d$n$\u9879\u548c$S_n$\uff0c\u5219$Sk$\u3001$S<\/em>{2k}-Sk$\u3001$S<\/em>{3k}-S_{2k}\u00b7\u00b7\u00b7$\u662f\u7b49\u5dee\u6570\u5217\u3002<\/p>\n\u7b49\u6bd4\u6570\u5217<\/h3>\n
\na_n=a_1q^{n-1} \\,\\, (q\u22601)
\n$$<\/p>\n
\nS_n=\\frac{a_1(1-q^n)}{1-q}
\n$$<\/p>\n
\n\u2461 $(ak,a<\/em>{k+m},a_{k+2m},\u00b7\u00b7\u00b7)$\u4e3a\u7b49\u6bd4\u6570\u5217\uff0c\u516c\u6bd4\u4e3a$q^k$(\u4e0b\u6807\u6210\u7b49\u5dee\u6570\u5217\uff0c\u5219\u5bf9\u5e94\u7684\u9879\u6210\u7b49\u6bd4\u6570\u5217)\uff1b
\n\u2462 \u6570\u5217$\\{\\lambda a_n\\}$($\\lambda$\u4e3a\u4e0d\u7b49\u4e8e\u96f6\u7684\u5e38\u6570)\u4ecd\u662f\u516c\u6bd4\u4e3a$q$\u7684\u7b49\u6bd4\u6570\u5217\uff1b\u82e5\u6709\u6b63\u9879\u7b49\u6bd4\u6570\u5217$\\{a_n\\}$\uff0c\u5219$\\{\\operatorname{log}a_n \\}$\u662f\u516c\u5dee\u4e3a$\\operatorname{log}(q)$\u7684\u7b49\u5dee\u6570\u5217\uff1b
\n\u2463 \u82e5$\\{a_n\\}$\u662f\u7b49\u6bd4\u6570\u5217\uff0c\u5219$\\{ka_n\\}$\u3001$\\{a_n^2\\}$\u3001$\\{\\frac{1}{a_n}\\}$\u3001$\\{a_n^r\\}(r \\in Z)$\u4e5f\u662f\u7b49\u5dee\u6570\u5217\uff0c\u516c\u6bd4\u4f9d\u6b21\u662f$q,q^2,\\frac{1}{q},q^r$\uff1b
\n\u2464 \u5355\u8c03\u6027\uff1a$\\{a_n\\}$\u7684\u516c\u6bd4\u4e3a$q$\uff0c\u5219\uff1a
\n1) $a_1 > 0, q > 1$\u6216$a_1 < 0, 0 < q < 1 \\Rightarrow \\{a_n\\}$\u4e3a\u9012\u589e\u6570\u5217\uff1b
\n2) $a_1 > 0, 0 < q < 1$\u6216$a_1 < 0, q >1 \\Rightarrow \\{a_n\\}$\u4e3a\u9012\u51cf\u6570\u5217\uff1b
\n3) $q=1 \\Rightarrow \\{a_n\\}$\u4e3a\u5e38\u6570\u5217\uff1b
\n4) $q<0 \\Rightarrow \\{a_n\\}$\u4e3a\u6446\u52a8\u6570\u5217\uff1b
\n\u2465 \u65e2\u662f\u7b49\u5dee\u6570\u5217\u53c8\u662f\u7b49\u6bd4\u6570\u5217\u7684\u6570\u5217\u662f\u5e38\u6570\u5217\uff1b
\n\u2466 \u82e5\u7b49\u6bd4\u6570\u5217$\\{a_n\\}$\u7684\u524d$n$\u9879\u548c$S_n$\uff0c\u5219$Sk$\u3001$S<\/em>{2k}-Sk$\u3001$S<\/em>{3k}-S_{2k}$\u00b7\u00b7\u00b7\u662f\u7b49\u6bd4\u6570\u5217\u3002<\/p>\n\u4e0d\u7b49\u5f0f<\/h2>\n
\u4e0d\u7b49\u5173\u7cfb\u4e0e\u4e0d\u7b49\u5f0f<\/h3>\n
\n\u2461 \u4f20\u9012\u6027 $a > b, b > c \\Rightarrow a > c$
\n\u2462 \u53ef\u52a0\u6027 $a > b \\Rightarrow a+c > b+c$
\n \u540c\u5411\u53ef\u52a0\u6027 $a > b, c > d \\Rightarrow a+c > b+d$
\n \u5f02\u5411\u53ef\u51cf\u6027 $a > b, c < d \\Rightarrow a-c > b-d$
\n\u2463 \u53ef\u79ef\u6027 $a > b, c > 0 \\Rightarrow ac > bc$
\n $a > b, c < 0 \\Rightarrow ac < bc$
\n\u2464 \u540c\u5411\u6b63\u6570\u53ef\u4e58\u6027 $a > b > 0,c > d > 0 \\Rightarrow ac>bd$
\n \u5f02\u5411\u6b63\u6570\u53ef\u9664\u6027 $a > b > 0,0 < c < d \\Rightarrow \\frac{a}{c} > \\frac{b}{d}$
\n\u2465 \u5e73\u65b9\u6cd5\u5219 $a > b >0 \\Rightarrow a^n > b^n \\, (n \\in N,\u4e14n>1)$
\n\u2466 \u5f00\u65b9\u6cd5\u5219 $a > b >0 \\Rightarrow \\sqrt[n]{a} > \\sqrt[n]{b} \\, (n \\in N,\u4e14n>1)$
\n\u2467 \u5012\u6570\u6cd5\u5219 $a > b >0 \\Rightarrow \\frac{1}{a} < \\frac{1}{b} ;\\, a < b < 0 \\Rightarrow \\frac{1}{a} > \\frac{1}{b}$<\/p>\n\u4e0d\u7b49\u5f0f\u8bc1\u660e\u7684\u51e0\u79cd\u5e38\u7528\u65b9\u6cd5<\/h3>\n
\n\u5176\u4ed6\u65b9\u6cd5\u6709\uff1a\u6362\u5143\u6cd5\u3001\u53cd\u8bc1\u6cd5\u3001\u7f29\u653e\u6cd5\u3001\u6784\u9020\u6cd5\u3001\u51fd\u6570\u5355\u8c03\u6027\u6cd5\u3001\u6570\u5b66\u5f52\u7eb3\u6cd5\u7b49<\/p>\n","protected":false},"excerpt":{"rendered":"