Question

How to solve the infinite series:

Answer 1

∞
∑3(1/4)ⁿ⁻¹   ==> replace n by consecutive values, starting with 1
ⁿ=¹
f(1) = 3(1/4)⁰ = 3 x 1 (any number raised to o is equal to 1
f(2) = 3(1/4)¹ = 3 x 1/4
f(3) = 3(1/4)² = 3 x (1/4)²
f(4) = 3(1/4)³ = 3 x (1/4)³
f(5) = 3(1/4)⁴ = 3 x (1/4)⁴
And so on and so forth. Then we have found a pattern that is:

f(n) = 3(1/4)ⁿ⁻¹ 
and with this you can find any number providing you know n