note that
(1-r^n) = (1-r)(1 + r + r^2 + r^3 + .....)
as n→∞ 1-r^n → 1
and the second factor on the right is the sum of the infinite series.
see what you can do with that.
How to prove the formal to find the infinite geometric series is correct?
3 answers
I still don't understand :(
c'mon -- the sum is
a + ar + ar^2 + ar^3 + ...
= a (1 + r + r^2 + r^3 + ...)
now recall that
(1-r^n) = (1-r)(1 + r + r^2 + r^3 + ...)
so the sum is the limit as n→∞ of
a(1-r^n)/(1-r) = a/(1-r)
if you're still unconvinced, you can find more proofs online.
Or probably in your class text.
a + ar + ar^2 + ar^3 + ...
= a (1 + r + r^2 + r^3 + ...)
now recall that
(1-r^n) = (1-r)(1 + r + r^2 + r^3 + ...)
so the sum is the limit as n→∞ of
a(1-r^n)/(1-r) = a/(1-r)
if you're still unconvinced, you can find more proofs online.
Or probably in your class text.
1 answer