AP EAMCET · Maths · Binomial Theorem
If \((1+x)^{15}=a_0+a_1 x+\ldots+a_{15} x^{15}, \quad\) then \(\sum_{r=1}^{15} r \frac{a_r}{a_r-1}\) is equal to
- A 110
- B 115
- C 120
- D 135
Answer & Solution
Correct Answer
(C) 120
Step-by-step Solution
Detailed explanation
Given that \(\begin{aligned} &(1+x)^{15}=a_0+a_1 x+a_2 x^2+\ldots+a_{15} x^{15} \\ & \Rightarrow \quad{ }^{15} C_0+{ }^{15} C_1 x+{ }^{15} C_2 x^2+\ldots+{ }^{15} C_{15} x^{15} \\ &=a_0+a_1 x+a_2 x^2+\ldots+a_{15} x^{15} \end{aligned}\) Equating the coefficient of various powers…
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