Sum of infinite series

If you noticed, without the summation notation, it is the present value money formula with finite time period.
PV - present value
FV - future value
i - interest rate
n - number of years
PV = FV/(1+i)^n

The present value money formula with indefinite time period is
PV = D / i
D - dividend (which is FV every year)

I'm curious if the infinite summation of FV/(1+i)^n (see the picture attached) is D / i.
Step by step process and explanation appreciated.

  • Your question is vague. Do you want to compute the sum in the attached picture? What is x?

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