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
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
- 32
- 64
- 128
- None of these
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The Correct Option is D
Solution and Explanation
Answer (d) None of these
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Concepts Used:
Binomial Theorem
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
Properties of Binomial Theorem
- 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 xn and 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.