Sum of the series 3 + 5 + 9 + 17 + 33 + ..... to n terms is

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Solution

The correct option is B
$S_{n} = 3 + 5 + 9 + 17 + 33 + . . . . .$
$= (2 + 1) + (2^{2} + 1) (2^{3} + 1) + (2^{4} + 1) + . . . .$
$= (2 + 2^{2} + 2^{3} + 2^{4} + . . . . n t e r m s) + n$
$= 2 (2^{n} - 1) + n = 2^{n + 1} + n - 2$
$= 2^{n + 1} + n - 2$

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