Binomial series

[Aniruddha Bardhan]

See the attachment.

My approach:

let S=20C0+20C1+...+20C10

20C0+20C1+...+20C20=2^20

2S-20C10=2^20

S=2^19+.5*20C10

How option B is correct?

[A]

Hint :

You can try to use the identity that $$\binom{n}{0} + binom{n}{1} + ...... + binom{n}{n} = 2^n $$ and then manipulate the rest.

[Aniruddha Bardhan]

Ya I use this approach. But got S=2^19+ (1/2)*20C10

[Soumyadeep mandal]

well even I am getting the answer as 2^19 + (1/2)*(20C10).... I think the sum is till (20C9) only, then only we can get option 4 as the answer ...

 

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