1.

If `C_(0), C_(1), C_(2),C_(3),..., C_(n)` are the binomial coefficients in the expansion of `(C_(0))/(1)+(C_(2))/(3)+(C_(4))/(5)+(C_(6))/(7)+...,` is equal toA. `(2^(n+1))/(n+1)`B. `(2^(n+1)-1)/(n+1)`C. `(2^(n))/(n+1) `D. none of these

Answer» Correct Answer - c
From illustration 14 and 15, we have
`(C_(0))/(1)+(C_(1))/(2) +(C_(2))/(3) +...+(C_(n))/(n+1) = (2^(n+1)-1)/(n+1)`
and `(C_(0))/(1) + (C_(1))/(2) + (C_(2))/(3) - ... +(C_(n))/(n + 1)=(1)/(n+1)`
Adding these two, we get
`2((C_(0))/(1) + (C_(1))/(2) + (C_(2))/(3) +..... )=(2^(n+1))/(n + 1)`
`rArr (C_(0))/(1) + (C_(2))/(3) + (C_(4))/(5) +..... =(2^(n))/(n + 1)`.


Discussion

No Comment Found

Related InterviewSolutions