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Question:

The sum of coefficient of integral powers of x in the binomial expansion of (1+√x)^50 is :

1/2(350)

1/2(350+1)

1/2(350-1)

1/2(250+1)

Solution:

(1𕒶√x)50=50C0󔼺C1(2√x)+50C2(2√x)2.we need to find sum of even forms, soPut√x=1⟹(1𕒶)50=1=50C0󔼺C1(2)+50C2(2)2 (1)and√x=𕒵⟹(1+2)50=350=50C0+50C12+50C2(2)2.. (2)Adding (1) and (2) we get,350+1=2(50C0+50C2(2)2+)⇒(50C0+50C2(2)2+)=12(1+350)