Mathematics
Senior High
Solved
写真の質問に答えてください!
T
k=1
k2 = =n(n+1)(2n+1)の証明
証明
以下の恒等式を用いる
・k' - (k-1)' = 3k2 - 3k + 1
この恒等式を1~nまでを足し合わせると
k
1
2
n-1
3
3
n =
n n³
k3
13
23
n
(n-1)3 (n-2)3
(n-1)3
k=1
n
-
n
(k-1)3
03
13
3k²
左辺でそれぞれ打ち消しあい
1
=
n
=
n (n
=
k=1
k=1
となり、順番を変えると
=
=
n
k² = n³ + > 3k
k=1
3k2 -3k +1
3(1)² -3(1) +1
3(2)²
-3(2) +1
3(n-1)²-3(n-1)+1
3(n)²-3(n) +1
3k+n
1) n
n
この式の意味って
何ですか?
Answers
Were you able to resolve your confusion?
Users viewing this question
are also looking at these questions 😉


分かりました!ありがとうございます!