New Home › Forums › Math Olympiad - IOQM › Binomial series
Tagged: Binomial
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?
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.
Ya I use this approach. But got S=2^19+ (1/2)*20C10
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 ...
.
.