The sum of the series C 0 20 - C 1 20 + C 2 20 - C 3 20 + … + C 10 20 is equal to

Question

The sum of the series C 0 20 - C 1 20 + C 2 20 - C 3 20 + … + C 10 20 is equal to, - C 10 20, 1 2 C 10 20, 0, C 10 20

MARKS App · Accepted Answer

S = C 0 20 - C 1 20 + C 2 20 + … + C 10 20 We know that, C 0 20 - C 1 20 + C 2 20 - … + C 20 = 0 20 ⇒ 2 C 0 20 - C 1 + 20 C 2 + 20 … - C 9 20 + C 10 = 0 20 ⇒ C 0 20 - C 1 20 + C 2 20 … - C 9 20 = - 1 2 C 10 20 So, S = - 1 2 C 10 20 + C 10 20 = 1 2 C 10 20

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