1平方➕3平方+5平方+7平方+…+29平方=多少

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摘要 an=(2n-1)^2=4n^2-4n+1=4n(n+1) -8n +1=(4/3)[n(n+1)(n+2) -(n-1)n(n+1)] - 4[n(n+1) -(n-1)n] + 1Sn = a1+a2+...+an=(4/3)n(n+1)(n+2) - 4n(n+1) + n= (1/3)n[ 4(n+1)(n+2) - 12(n+1) +3 ]=(1/3)n(4n^2-1)=(1/3)n(2n-1)(2n+1)1^2+3^2+...+29^2=S15=(1/3)(15)(29)(31)=4495

咨询记录 · 回答于2023-02-12

1平方➕3平方+5平方+7平方+…+29平方=多少

an=(2n-1)^2=4n^2-4n+1=4n(n+1) -8n +1=(4/3)[n(n+1)(n+2) -(n-1)n(n+1)] - 4[n(n+1) -(n-1)n] + 1Sn = a1+a2+...+an=(4/3)n(n+1)(n+2) - 4n(n+1) + n= (1/3)n[ 4(n+1)(n+2) - 12(n+1) +3 ]=(1/3)n(4n^2-1)=(1/3)n(2n-1)(2n+1)1^2+3^2+...+29^2=S15=(1/3)(15)(29)(31)=4495

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