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Q.

The value of C01.3-C12.3+C23.3-C34.3+...+-1nCnn+1.3 is

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a

3n+1

b

n+13

c

13n+1

d

None of these

answer is C.

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Detailed Solution

We have to find the value of

C01.3C12.3+C23.3C34.3++(1)nCn(n+1)3

we have,

(1+x)n=C0+C1x+C2x2+..+Cnxn

Integrating both sides w.r.t.x , from -1 to 0, we get

10(1+x)ndx=10C0+C1x+C2x2+.+Cnxndx(1+x)n+1n+110=cosx+C1x22+..+Cnxn+1n+110C0C12+C22+.+(1)nCnn+1=1n+1 The given expression =13C0C12+C22.=131n+1=13(n+1)

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