f is a function such that f(x + y) = f(x) .f(y),`forall x, y in R` , if f(1) = 3, then find `sum_(r = 1)^n f(r)`.

Explanation

Here, f(x + y) = `f(x) cdot f(y)`
Putting x = 1 , y = 1 , we get
f(2) = `f(1) cdot f(1) = [f(1)]^2 = 3^2`
Again putting, x = 2 , y = 1 , we get
f(3) = `f(2) cdot f(1) = 3^2 cdot 3= 3^3`
`therefore sum_(r = 1)^n f(r) = sum_(r = 1)^n 3^r = (3(3^n - 1))/(3 - 1) = 3/2 (3^n - 1)`