Find the positive integer n satisfying ∑ k = 1 n k 2 k = 2 n + 10 + 2 .

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MathematicsSequence & SeriesA.G.P.Medium2 minQB

MathematicsMediumsingle choice

Find the positive integer $n$ satisfying $\sum_{k = 1}^{n} k 2^{k} = 2^{n + 10} + 2$ .

Answer:

Solution:

The geometric-arithmetic sum is $(n - 1) 2^{n + 1} + 2$ . Thus $(n - 1) 2^{n + 1} = 2^{n + 10}$ , so $n - 1 = 2^{9} = 512$ and $n = 513$ .

Stream:JEESubject:MathematicsTopic:Sequence & SeriesSubtopic:A.G.P.

⏱ 2mℹ️ Source: QB

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