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AP EAMCET2012MathematicsSequences and Series

1+ 1 3 2^2 + 1 5 2^4 + 1 7 2^6 + is equal to

Options

  1. A_e 2
  2. B_e 3
  3. C_e 4
  4. D_e 5

Correct answer

B. _e 3

Step-by-step solution

Given series is 1+ 1 3 2^2 + 1 5 2^4 + 1 7 2^6 + aligned & =2 [ 1 / 2 1 + (1 / 2)^3 3 + (1 / 2)^5 5 + ] & = _e ( 1+ 1 2 1- 1 2 )= _e ( 3 / 2 1 / 2 ) & [ _e ( 1+x 1-x )=2 (x+ x^3 3 + x^5 3 + ) ] & = _e 3 & aligned

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