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Find formula for sequence

Hi,

I need to find a formula for the sequence below by first finding a recurrence for a_n, then solving the recurrence.

Thanks!

a_n = 1/2 + 2/4 + 3/8 + 4/16 + 5/32 + · · · + n/(2^n) = sum_{k=1}^n (k /(2^k))

Solution Preview

let q_k=k/(2^k), then a_n=sum_{k=1}^n q_k
then 2a_n=1+1+3/4+4/8+5/16+...+n/2^(n-1)
then we ...

Solution Summary

This solution is comprised of a detailed explanation to first finding a recurrence for a_n, then solving the recurrence.

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