Question

up my questions please solve

Answer 1

Heya user,

Let x = 40C40 + 40C1 + 40C2 + ...

Note: nCr = nC(n-r)

.'. 40C1 = 40C39 and so on.

Now,
2x = [40C40 + 40C39 + ... + 40C21 + 40C20 + 40C19 + ... + 40C0 ] + 40C20

Now, consider the binomial expansion of [ 1 + 1 ]^40 which by Binomial theorem will have the above given co-efficients..

.'. We replace : -->

[40C40 + 40C39 + ... + 40C21 + 40C20 + 40C19 + ... + 40C0 ]  by 2^40

Hence, 2x = 2^40 + 40C20