JEE Mains · Maths · STD 12 - 1. relation and function
Suppose \(f\) is a function satisfying \(f ( x + y )= f ( x )+ f ( y )\) for all \(x , y \in N\) and \(f (1)=\frac{1}{5}\). If \(\sum \limits_{n=1}^m \frac{f(n)}{n(n+1)(n+2)}=\frac{1}{12}\), then \(m\) is equal to \(...............\).
- A \(11\)
- B \(12\)
- C \(10\)
- D \(13\)
Answer & Solution
Correct Answer
(C) \(10\)
Step-by-step Solution
Detailed explanation
\(\because f(1)=\frac{1}{5} \therefore f(2)=f(1)+f(1)=\frac{2}{5}\) \(f(2)=\frac{2}{5} \quad f(3)=f(2)+f(1)=\frac{3}{5}\) \(f(3)=\frac{3}{5}\) \(\therefore \sum \limits_{n=1}^m \frac{f(n)}{n(n+1)(n+2)}\)…
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