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Should this question
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I am stuck on this question from the IB Cambridge HL math text book about Mathematical induction. I am sorry about the bad formatting I am new and have no idea how to write the summation sign. Using mathematical induction prove that the $$\sum^n_{k=1} k2^k =(n-1)(2^{n+1})+2$$ [correction made...

be closed as duplicate of the following?
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Given $$1\cdot 2^1 + 2\cdot 2^2 + 3\cdot 2^3 + 4\cdot 2^4 + \cdots + d \cdot 2^d = \sum_{r=1}^d r \cdot 2^r,$$ how can we infer to the following solution? $$2 (d-1) \cdot 2^d + 2.$$ Thank you

The difference is that the first one asks for a proof using induction.