Are The Binomial Coefficients In The Expansion Of (1+x)15, Then C0 ...

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4. If C0, C1, C2, ldots, C15 are the binomial coefficients in the expansion of (1+x)15, then (C1/C0)+(2 C2/C1)+(3 C3/C2)+ ldots+(15 C15/C14) is equal to

Q. If C0​,C1​,C2​,…,C15​ are the binomial coefficients in the expansion of (1+x)15, then C0​C1​​+C1​2C2​​+C2​3C3​​+…+C14​15C15​​ is equal to 2041 244 AMUAMU 2015Binomial Theorem Report Error A

32

0% B

64

21% C

128

16% D

None of these

63%

Solution:

C0​C1​​+C1​2C2​​+C2​3C3​​+…+C14​15C15​​ =n+n22n(n−1)​​+2n(n−1)​3×23n(n−1)(n−2)​​+… upto 15 terms =n+(n−1)+(n−2)+…+ upto 15 terms =215(15+1)​=120