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if c0,c1,c2,.......cn donets the coefficients ofthe bin. expantion (1+x)^n, then the value of c1+3c3+5c5+... is

if c0,c1,c2,.......cn donets the coefficients ofthe bin. expantion (1+x)^n, then the value of
c1+3c3+5c5+... is

Grade:12

1 Answers

Badiuddin askIITians.ismu Expert
148 Points
14 years ago

Dear manan

from Binomial expansion we know that

(1+x)n =C0 + C1x + C2x2 +C3x3 +C4x4+C5x5+  ......Cnxn

now differentiate both side

n(1+x)n-1 = C1 +2C2x+3C3x2 +4C4x3 + 5C5x4 + ......

now put x=1

n2n-1 = C1 +2C2+3C3 +4C4 + 5C5 + ...... .............(1)

 

now put x=-1

0 =C1 -2C2+3C3 -4C4 + 5C5 + ...... .............(2)

 

(1) +(2)

n2n-2 = C1 +3C3  + 5C5 + ...... ............

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Badiuddin

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