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The sum of the series 1+ 4 3 + 10 9 + 28 27 + upto n terms is

Options

  1. A7 6 n+ 1 6 - 2 3.2^ n-1
  2. B5 3 n- 7 6 + 1 2.3^ n-1
  3. Cn+ 1 2 - 1 2.3^n
  4. Dn- 1 3 - 1 3.2^ n-1

Correct answer

C. n+ 1 2 - 1 2.3^n

Step-by-step solution

Given series is 1+ 4 3 + 10 9 + 28 27 + . n terms =1+ (1+ 1 3 )+ (1+ 1 9 )+ (1+ 1 27 )+ . n terms =(1+1+1+ +n terms )+ ( 1 3 + 1 9 + 1 27 + n . terms )=n+ 1 3 (1- 1 3^n ) 1- 1 3 =n+ 1 3 3 2 [1-3^ -n ]=n+ 1 2 [1-3^ -n ]=n+ 1 2 - 1 2.3^n

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