Question

An infinite geometric progression is such that the sum of all the terms after the nth is equal to twice the nth term. Show that the sum to infinity of the whole progression is three times the first term.

Answer 1

@experimentX @electrokid

Answer 2

set up the problem..
\[
\sum_{k=n}^\infty a_k=2\times\sum_{k=0}^{n-1}a_k
\]

Answer 3

\[S_\infty-S_n=2\times S_n\\
\implies S_\infty=3\times S_n
\]

Answer 4

hold on..
twice the "nth" term or twice the "sum of first n terms"?

Answer 5

It's twice the nth term.