Prove the following identities
1*2^0 + 2*2^1 + 3*2^2 + . . . + n*2^2n-1= (n-1)2^n + 1
Also
1 + 3 + 9 + 27 + . . . + 3^n-1= (3n-1)
2
Hello, taylor1234!
There is a typo in the first one . . . the general term is not correct.
In each term, the exponent is one less than the coefficient: .
We have: . . . . .
Multiply by 2: .
Subtract [2] - [1]: .
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