Question
The value of C12 + C34 + C56 + ...... is equal to
Answer: Option A
:
A
We know that
(1+x)n−(1−x)n2 = C1x+C3x3+C5x5+........
Integrating from x = 0 to x = 1, we get
12∫10(1+x)n−(1−x)ndx
=∫10(C1x+C3x3+C5x5+.......)dx
⇒ 12{(1+x)n+1n+1+(1−x)n+1n+1}10=C12 +C34 + C56 + ....
orC12 +C34 + C56 + .......=12 {2n+1−1n+1 +0−1n+1}
=12 2n+1−2n+1 =2n−1n+1
Was this answer helpful ?
:
A
We know that
(1+x)n−(1−x)n2 = C1x+C3x3+C5x5+........
Integrating from x = 0 to x = 1, we get
12∫10(1+x)n−(1−x)ndx
=∫10(C1x+C3x3+C5x5+.......)dx
⇒ 12{(1+x)n+1n+1+(1−x)n+1n+1}10=C12 +C34 + C56 + ....
orC12 +C34 + C56 + .......=12 {2n+1−1n+1 +0−1n+1}
=12 2n+1−2n+1 =2n−1n+1
Was this answer helpful ?
More Questions on This Topic :
Latest Videos
Latest Test Papers
Submit Solution