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Question

If (1+x)15=C0+C1x+C2x2+......+C15x15, then C2+2C3+3C4+......+14C15=

A
14.214
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B
13.214+1
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C
13.2141
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D
None of these
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Solution

The correct option is B 13.214+1

We have (1+x)15=C0+C1x+C2x2+......+C15x15
(1+x)151x=C1+C2x+....+C15x14
Differentiating both sides with respect to x, we get
=x.15(1+x)14(1+x)15+1x2
=C2+2C3x+........+14C15x13
putting x=1, we get
C2+2C3+....+14C15=15.214215+1=13.214+1.


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