Plz solve it. This is question of binomial theorem. I want 2 methods differentiation one and other sigma method by finding rth term.

For differentiation method.
Step 1. Replace x by x2 in the (1+x)2 expansion.
Step 2. Multiply above equation by x.
Step 3. Replace x by -1 you will get your answer.

For General term method
Its r+1th term will be Tr+1 = (-1)^r (2r+1)Cr
Now apply the summation, then S =2* sum (-1)^r(rCr) + sum(-1)^rCr.
from above we can easily say that second term i.e. sum(-1)^r Cr = 0 and first term we can get if we differentation (1+x)^r and replace x = -1.

Thanks,