Are Binomial Coefficients Of Order N, Then The Value Of 2C1

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4. If C0,C1, C2, ....,Cn are binomial coefficients of order n, then the value of (C1/2)+(C3/4)+(C5/6)+...=

Q. If C0​,C1​,C2​,....,Cn​ are binomial coefficients of order n, then the value of 2C1​​+4C3​​+6C5​​+...= 2225 176 COMEDKCOMEDK 2009Binomial Theorem Report Error A

n+12n+1​

16% B

n+12n−1​

46% C

n−12n+1​

18% D

n+12n​

20%

Solution:

2C1​​+4C3​​+6C5​​+...=1⋅2n​ +1⋅2⋅3⋅4n(n−1)(n−2)​1⋅2⋅3⋅4⋅5⋅6+n(n−1)(n−2)(n−3)(n−4)​+..... =(n+1)1​[2!n(n+1)​+4!n(n−1)(n−2)(n+1)​+...] =n+11​[n+1C2​+n+1C4​+......] =n+11​[2n+1−1−1]=n+12n−1​