Find ∑_t=1^39 f(t) if f: R arrow R is defined as f(x+y)=f(x)+f(y), x, y ∈ R and f(I)=7

Question

MARKS Content Team · Accepted Answer

Correct answer: (B) 5460. It is given that, f(x+y)=f(x)+f(y) and f(1)=7 f(x)=7 x ∴ f(x)=7 x So, ∑_t=1^39 f(t) =7[1+2+3+…+39] =7 × (39 × 40)/2=5460.

Find \(\sum_{t=1}^{39} f(t)\) if \(f: \mathbf{R} \rightarrow \mathbf{R}\) is defined as \(f(x+y)=f(x)+f(y), x, y \in \mathbf{R}\) and \(f(\mathrm{I})=7\)