Question

已知数列{an}中a1=1 an+1=an+2^n-1求an

an+1， n+1为下标。很急。谢谢啦。

Answer 1

a(n+1)=an+2^n-1
a(n+1)-an=2^n-1
an-a1
=(an-a(n-1))+(a(n-1)-a(n-2))+……+a2-a1
=2^n+2^(n-1)+……+2-(n-1)
=2^n-2-n+1
=2^n-n-1
得an=2^n-n
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