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The sum of the series 2 1 · 2 + 5 2 · 3 · 2 + 10 3 · 4 · 2 2 + 17 4 · 5 · 2 3 + ...... to n terms is

Options

  1. An n + 1 · 2 n + 1
  2. Bn + 1 n · 2 n + 1
  3. Cn n + 1 · 2 n
  4. Dn + 1 n · 2 n

Correct answer

C. n n + 1 · 2 n

Step-by-step solution

The required sum = ∑ r = 1 n r 2 + 1 r r + 1 2 r - 1 = ∑ r = 1 n 2 r r + 1 - r - 1 r 2 r - 1 = ∑ r = 1 n r r + 1 2 r - r - 1 r 2 r - 1 = n n + 1 · 2 n

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