Question

How do you prove the formula for the sum of an infinite converging series? S∞=a1/1-r

Answer 1

Step-by-step explanation:

so the infinite series is

a + ar + ar^2 + ar^3....

= a(1 + r + r^2 + r^3...)

= a(1 + r(1 + r + r^2 + r^3...))

ignore the a for a second

imagine it's 1

we call this sum S

S = 1 + r(1 + r + r^2 + r^3...)

S = 1 + rS

S - rS = 1

S(1 - r) = 1

S = 1/(1-r)

and the difference for that series is every term is multiplied by a

or S = a/(1-r)