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find general term formula for sequence

Source: China south east mathematical olympiad 2008 day1 problem 2

July 14, 2013

algebra unsolvedalgebra

Problem Statement

Let

\{a_n\}

be a sequence satisfying:

a_1=1

and

a_{n+1}=2a_n+n\cdot (1+2^n),(n=1,2,3,\cdots)

. Determine the general term formula of

\{a_n\}