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The sum of n terms of the series, 4 3 + 10 9 + 28 27 + is

Options

  1. A3^n(2 n+1)+1 2 (3^n )
  2. B3^n(2 n+1)-1 2 (3^n )
  3. C3^n n-1 2 (3^n )
  4. D3^n-1 2

Correct answer

B. 3^n(2 n+1)-1 2 (3^n )

Step-by-step solution

Given series is 4 3 + 10 9 + 28 27 + The sum of the given series upto n -terms aligned & 4 3 + 10 9 + 28 27 + . upto n -terms & = (1+ 1 3 )+ (1+ 1 9 )+ (1+ 1 27 )+ upto n -terms & =(1+1+1+ upto n -terms ) & + ( 1 3 + 1 3^2 + 1 3^3 + upto n - terms ) & =n+ 1 3 ( 1- 1 3^n 1- 1 3 )=n+ (3^n-1 ) 2 (3^n ) = 3^n(2 n+1)-1 2 (3^n ) aligned

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