Progression (Sequence and Series)Hard
Question
The sum of the series
20C0 20C1 + 20C2 - 20C3 + .... - .... + 20C10 is
20C0 20C1 + 20C2 - 20C3 + .... - .... + 20C10 is
Options
A.- 20C10
B.
20C10
20C10 C.0
D.20C10
Solution
(1 + x)20 = 20C10 + 20C1x + ... +20C10x10 + .... +20C20x20
put x = - 1,
0 = 20C10 - 20C1 + .... - 20C9 + 20C10 - 20C11 + .... + 20C20
0 = 2 (20C0 - 20C1 + .... - 20C9) + 20C10
⇒ 20C0 - 20C1 + .... + 20C10 = 20C10.
put x = - 1,
0 = 20C10 - 20C1 + .... - 20C9 + 20C10 - 20C11 + .... + 20C20
0 = 2 (20C0 - 20C1 + .... - 20C9) + 20C10
⇒ 20C0 - 20C1 + .... + 20C10 =
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