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AP EAMCET2008MathematicsSequences and Series

1 1 3 + 1 2 5 + 1 3 7 + 1 4 9 + is equal to

Options

  1. A2 _e 2-2
  2. B2- _e 2
  3. C2 _e 4
  4. D_e 4

Correct answer

B. 2- _e 2

Step-by-step solution

aligned & Let S= 1 1 3 + 1 2 5 + 1 3 7 + 1 4 9 + & T_n= 1 n(2 n+1) & = 1 n - 2 (2 n+1) & S= _ n=1 ^ T_n= _ n=1 ^ ( 1 n - 2 2 n+1 ) & = 1 1 - 2 3 + 1 2 - 2 5 + 1 3 - 2 7 + 1 4 - 2 9 + 1 5 - & =1+ 1 2 - 1 3 + 1 4 - 1 5 + & =1- (- 1 2 + 1 3 - 1 4 + 1 5 - ) & =1- (-1+ _e 2 )=2- _e 2 & aligned

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