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Question

If (1+x)n=C0+C1x+C2x2+....+Cnxn, then the value of C0+2C1+3C2+....+(n+1)Cn will be

A
(n+2)2n1
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B
(n+1)2n
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C
(n+1)2n1
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D
(n+2)2n
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Solution

The correct option is A (n+2)2n1
Since we know that 2n=Cn0+Cn1+Cn2+Cn3+Cn4+Cn5+....=r=nr=oCnrCn0+2Cn1+3Cn2+4Cn3+5Cn4+6Cn5+....=nr=0(r+1)Cnr=nr=0(r)Cnr+r=nr=oCnrrCnr=nCn1r1nr=0(r+1)Cnr=n2n1+2n=(n+2)2n1

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