AP EAMCET · Maths · Functions
If \(f: R \rightarrow R\) is defined as \(f(x+y)=f(x)+f(y)\), \(\forall x, y \in R\) and \(f(\mathrm{l})=5\), then find the value of the following \(\sum_{r=1}^n f(r)\) is equal to
- A \(\frac{5 n(n+1)}{2}\)
- B \(\frac{7 n(n-1)}{2}\)
- C \(\frac{5 n(n-1)}{2}\)
- D \(\frac{7 n(n+1)}{2}\)
Answer & Solution
Correct Answer
(A) \(\frac{5 n(n+1)}{2}\)
Step-by-step Solution
Detailed explanation
\[ \text { Given } f: R \rightarrow R \text { is defined as } \] \[ f(x+y)=f(x)+f(y), \forall x, y \in R \text { and } f(1)=5 \] To Find \(\sum_{r=1}^n f(r)=\) ? Since, \(f(x+y)=f(x)+f(y)\) Let \(x=y=1\)…
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