题目

用数学归纳法证明1+2+22+23+…+25n-1(n∈N*)是31的倍数时,从“n=k到n=k+1”需添的项是__________. 答案：解析:当n=k时,1+2+22+…+25k-1,当n=k+1时,1+2+22+…+25k-1+25k+…+25(k+1)-1,∴增加项为25k+25k+1+…+25k+4.答案:25k+25k+1+…+25k+4

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