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Question

Find sum of series 20C020C1+20C220C3+..........+20C10

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Solution

To find:- 20C020C1+20C220C3+..........+20C10
Solution:-
As we know that,
(1+x)20=20C0+20C1x+20C2x2+20C3x3+.....+20C20x20
Substituting x=1 in the above equation, we have
(1+(1))20=20C0+20C1(1)+20C2(1)2+.....+20C20(1)20
0=20C020C1+20C220C3+..........+20C20
2(20C020C1+20C220C3+.....20C9)+20C10=0
2(20C020C1+20C220C3+.....20C9+20C10)=20C10
20C020C1+20C220C3+.....20C9+20C10=1220C10
Hence the value of 20C020C1+20C220C3+..........+20C10 is 1220C10.

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