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KCET2024MathematicsSequences and Series

If S_n stands for sum to n -terms of a GP with a as the first term and r as the common ratio, then S_n: S_ 2 n is

Options

  1. Ar^n+1
  2. B1 r^n+1
  3. Cr^n-1
  4. D1 r^n-1

Correct answer

B. 1 r^n+1

Step-by-step solution

S_n= a (1-r^n ) 1-r S_ 2 n = a (1-r^ 2 n ) 1-r S_n S_ 2 n = a (1-r^n ) 1-r 1-r a (1-r^ 2 n ) = 1-r^n (1+r^n ) (1-r^n ) Hence, S_n: S_ 2 n = 1 1+r^n

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