Question:

If $C_o, C_1,C_2,....C_{15}$ are the binomial coefficients in the expansion of $(1+x)^{15}$ then $\frac {C_1}{C_o} +\frac {2C_2}{C_1}+\frac {3C_3}{C_2} +....+\frac {15C_{15}}{C_{14}}$ is equal to

Updated On: Jun 14, 2022

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The Correct Option is D

Answer (d) None of these

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The binomial theorem formula is used in the expansion of any power of a binomial in the form of a series. The binomial theorem formula is

The number of coefficients in the binomial expansion of (x + y)ⁿ is equal to (n + 1).
There are (n+1) terms in the expansion of (x+y)ⁿ.
The first and the last terms are xⁿand yⁿ respectively.
From the beginning of the expansion, the powers of x, decrease from n up to 0, and the powers of a, increase from 0 up to n.
The binomial coefficients in the expansion are arranged in an array, which is called Pascal's triangle. This pattern developed is summed up by the binomial theorem formula.