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.

Question

anonymous · Answer

@experimentX  @electrokid

anonymous · Answer

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

anonymous · Answer

$$S_\infty-S_n=2\times S_n\
\implies S_\infty=3\times S_n
$$

anonymous · Answer

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

anonymous · Answer

It's twice the nth term.