JEE Mains · Maths · STD 12 - 5. continuity and differentiation
Let \(f ( x )=\sum \limits_{ k =1}^{10} kx ^{ k }, x \in R\). If \(2 f(2)+f^{\prime}(2)=119(2)^{ n }+1\) then \(n\) is equal to \(..........\).
- A \(9\)
- B \(10\)
- C \(8\)
- D \(7\)
Answer & Solution
Correct Answer
(B) \(10\)
Step-by-step Solution
Detailed explanation
\(f(x)=\sum \limits_{k=1}^{10} k x^k\) \(f(x)=x+2 x^2+\ldots \ldots \ldots+10 x^{10}\) \(f(x) . x=x^2+2 x^3+\ldots \ldots \ldots+9 x^{10}+10 x^{11}\) \(f(x)(1-x)=x+x^2+x^3+\ldots \ldots \ldots+x^{10}-10 x^{11}\)…
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