$已知数列{an}的通项公式an=n²+n,则{an}的前n项和Sn=?_知道$

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已知数列{an}的通项公式an=n²+n,则{an}的前n项和Sn=?

学习时间:2026-09-29 03:08:53 阅读：9868

已知数列{an}的通项公式an=n²+n,则{an}的前n项和Sn=?

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诚心的白开水

秀丽的眼睛

2026-09-29 03:08:53

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an =n^2+n = n(n+1) = (1/3)[n(n+1)(n+2) - (n-1)n(n+1)]Sn = (1/3){ summation (i:1->n)[i(i+1)(i+2) - (i-1)i(i+1)] } = (1/3)n(n+1)(n+2)

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2026-09-29 03:08:53
an =n^2+n = n(n+1) = (1/3)[n(n+1)(n+2) - (n-1)n(n+1)]Sn = (1/3){ summation (i:1->n)[i(i+1)(i+2) - (i-1)i(i+1)] } = (1/3)n(n+1)(n+2)

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