Q.

Sum of the last 30 coefficients of powers of x in the binomial expansion of (1+x)59 is

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a

229

b

228

c

259-229

d

258

answer is D.

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Detailed Solution

Let S= some of the last 30 coefficients in (1+x)59=59C30+59C31+…+59C59                                 (1)Using  nCr=nCn−r, we getS=59C29+59C28+…+59C0                               (2)Adding (1) and (2), we get2S=59C0+59C1+…+59C59=259⇒S=258
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Sum of the last 30 coefficients of powers of x in the binomial expansion of (1+x)59 is