Question

Prove using mathematical induction that for all n ? 1: ?_{r=1}^{n} (r + 1) ? 2^{r-1} = n ? 2^n

          Prove using mathematical induction that for all n ? 1:
?_{r=1}^{n} (r + 1) ? 2^{r-1} = n ? 2^n

Added by Josep R.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Madhur L

06/12/2023

Step 1

We need to show that the equation holds true for n = 1. (r+1)2^1 - 1 = 1 * 2 * 1 - 1 2(r+1) - 1 = 2 2r + 2 - 1 = 2 2r + 1 = 2 r = 0.5 Since the equation holds true for n = 1, the base case is proven. Show more…

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Prove using mathematical induction that for all n ≥ 1: ∑_{r=1}^{n} (r + 1) ∙ 2^{r-1} = n ∙ 2^n

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Prove using mathematical induction that for all n ? 1: ?_{r=1}^{n} (r + 1) ? 2^{r-1} = n ? 2^n

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