The sum of the first 20 terms of the series 1 + 3 2 + 7 4 + 15 8 + 31 16 + … is

Question

The sum of the first 20 terms of the series 1 + 3 2 + 7 4 + 15 8 + 31 16 + … is, 39 + 1 2 19, 38 + 1 2 20, 38 + 1 2 19, 39 + 1 2 20

MARKS App · Accepted Answer

1 + 3 2 + 7 4 + 15 8 + 31 16 + … = 2 - 1 + 2 - 1 2 + 2 - 1 4 + 2 - 1 8 + 2 - 1 16 + … u p t o 20 t e r m s = 40 - 1 + 1 2 + 1 4 + 1 8 + … u p t o 20 t e r m s = 40 - 1 - 1 2 20 1 - 1 2 = 40 - 2 + 1 2 19 = 38 + 1 2 19

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