Mathematics
Senior High
Resolved
紫と黄色の式の式変形の仕方をおしえてください
第早 数列
例題 次の和を求めよ。
6
解
800
この和は,第k項がk (k+1) である数列の初項から第n
項までの和であるから
G
=
1・2+2²・3+3%•4+…………+n²(n+1)
n
n
n
n
Σ k²(k+1)= Σ (k³+k²) = Σ k³+ Σ k²
k=1
k=1
k=1
k=1
={/12/n(n+1)}'+1/n(n+1)(2n+1)
-n(n+1){3n(n+1)+2(2n+1)}
1
12
1/2 n(n-
_n(n+1)(3n²+7n+2) = √2n(n+1)(n+2)(3n+1)
02-0 K = (0
+03
次の和を求めよ。
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