Question

求数列5/4,33/16,193/64,…,（n+1/4^n）,…的前n项和.

Answer 1

an=n+1/4^n

Sn=(1+2+3···+n)+[1/4 *(1+1/4^n)] / (1+1/4)

=n(n+1)/2 +[1/4 + 1/4^(n+1)] *4/5

=n^2 / 2 +n/2 +1/5 +1/(5*4^n)

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