1*3,2*4,3*5,...n(n+2)求数列的前n项和Sn的详细步骤,最好有,每一步,答案是n(n+1)(2n+7)/6
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![1*3,2*4,3*5,...n(n+2)求数列的前n项和Sn的详细步骤,最好有,每一步,答案是n(n+1)(2n+7)/6](/uploads/image/z/644039-71-9.jpg?t=1%2A3%2C2%2A4%2C3%2A5%2C...n%28n%2B2%29%E6%B1%82%E6%95%B0%E5%88%97%E7%9A%84%E5%89%8Dn%E9%A1%B9%E5%92%8CSn%E7%9A%84%E8%AF%A6%E7%BB%86%E6%AD%A5%E9%AA%A4%2C%E6%9C%80%E5%A5%BD%E6%9C%89%2C%E6%AF%8F%E4%B8%80%E6%AD%A5%2C%E7%AD%94%E6%A1%88%E6%98%AFn%EF%BC%88n%2B1%EF%BC%89%EF%BC%882n%2B7%EF%BC%89%2F6)
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1*3,2*4,3*5,...n(n+2)求数列的前n项和Sn的详细步骤,最好有,每一步,答案是n(n+1)(2n+7)/6
1*3,2*4,3*5,...n(n+2)求数列的前n项和Sn的详细步骤,最好有,每一步,答案是n(n+1)(2n+7)/6
1*3,2*4,3*5,...n(n+2)求数列的前n项和Sn的详细步骤,最好有,每一步,答案是n(n+1)(2n+7)/6
原式=1×(1+2)+2×(2+2)+3×(3+2)+……+n(n+2)
=1²+2²+3²+……+n²+2×(1+2+3+……+n)
=1/6×n(n+1)(2n+1)+n(n+1)
=1/6n(n+1)(2n+7)
an=n(n+2)=n²+2n
且1²+2²+..+n²=n(n+1)(2n+1)/6
则
Sn=1²+2+2²+2x2..+n²+2n
=(1²+2²+..+n²)+2(1+2+..+n)
=n(n+1)(2n+1)/6+n(n+1)
=n(n+1)[(2n+1)+6]/6
=n(n+1)(2n+7)/6