SOLUTION: I have this sum: 1 + 4 + 12 + 32 + ... + 2^(n-1)*n I haven't done calculus in a while so I can't remember how to do it ( 2^(n-1)*n = 2 to the power of (n-1), everything times n

SOLUTION: I have this sum: 1 + 4 + 12 + 32 + ... + 2^(n-1)n I haven't done calculus in a while so I can't remember how to do it ( 2^(n-1)n = 2 to the power of (n-1), everything times n

Question 837300: I have this sum:
1 + 4 + 12 + 32 + ... + 2^(n-1)*n
I haven't done calculus in a while so I can't remember how to do it
( 2^(n-1)*n = 2 to the power of (n-1), everything times n )
Cheers
Answer by richard1234(7193) (Show Source): You can put this solution on YOUR website!
Break up the sum as follows:

Each of the summations on the RHS is a geometric series, which can be evaluated with some algebra.
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