已知等差数列{an}满足:a1+a2+a3+…+a101=0,则使前n项和Sn取得最大值的n值为A.50B.51C.50或51D.51或52

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已知等差数列{an}满足:a1+a2+a3+…+a101=0,则使前n项和Sn取得最大值的n值为A.50B.51C.50或51D.51或52
已知等差数列{an}满足:a1+a2+a3+…+a101=0,则使前n项和Sn取得最大值的n值为A.50B.51C.50或51D.51或52

已知等差数列{an}满足:a1+a2+a3+…+a101=0,则使前n项和Sn取得最大值的n值为A.50B.51C.50或51D.51或52
加条件a1>0吧
∵等差数列{an},设公差为d
∴a1+a2+a3+…+a101
=S101=(a1+a101)*101/2=0
∴a1+a101=0
∴a1+a1+100d=0
∴a1=-50d,a1>0,d0,a51=0,从a52开始an

本题还应加上条件: 公差d<0

a1+a2+a3+…+a101=0
a1+a101=a2+100=a3+a99=……=a50+a52=2a51
a1+a2+a3+…+a101=101*a51
a51=0
所以选C

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