1乘2+2乘3+·········100乘101=多少

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1乘2+2乘3+·········100乘101=多少

1乘2+2乘3+·········100乘101=多少
1乘2+2乘3+·········100乘101=多少

1乘2+2乘3+·········100乘101=多少
an=n(n+1)=n^2+n
Sn=(1+2+..+n)+(1+2^2+3^2+...+n^2)
=n(n+1)/2+n(n+1)(2n+1)/6
=n(n+1)(n+2)/3
n=100
S100=343400

令An=n(n+1)=n^2+n
Sn
=A1+A2+……An
=(1+2+..+n)+(1+2^2+3^2+...+n^2)
=n(n+1)/2+n(n+1)(2n+1)/6
=n(n+1)(n+2)/3
∵n=100
∴Sn=S100=343400