The sum of ordinary annuity is given by
$F = \dfrac{A[ \, (1 + i)^n - 1 \, ]}{i}$
To learn more about annuity, see this page: ordinary annuity, deferred annuity, annuity due, and perpetuity.
Derivation
$F = \text{ Sum}$
$F = A + F_1 + F_2 + F_3 + \cdots + F_{n-1} + F_n$
$F = A + A(1 + i) + A(1 + i)^2 + A(1 + i)^3 + \cdots + A(1 + i)^{n-1} + A(1 + i)^n$