DOES THE FOLLOWING INFINITE SERIES CONVERGE OR DIVERGE? EXPLAIN YOUR ANSWER. (1/5)+(1/15)+(1/45)+(1/81)

Question

amistre64 · Answer

i dont see a way to compare it to something sensible as is

psymon · Answer

I can't catch on to a pattern personally. At least not yet.

amistre64 · Answer

1/(5n)  might be a sound comparison ....

amistre64 · Answer

or 1/(5*3^n) ?

psymon · Answer

I was looking at that one before, too, but wasn't sure.

amistre64 · Answer

the scant sequence provided doesnt lend much to comparison tho

psymon · Answer

It looks like some sort of p-series could work, though.

amistre64 · Answer

psymon · Answer

Joy :/

anonymous · Answer

$$1/5+1/15+1/45+...=1/5(1+1/3+1/3^2+...)=1/5\sum_{n=0}^{\infty} (1/3)^n$$$$=1/5 \times 1/(1-1/3)=3/10$$

psymon · Answer

The two series go different routes starting at n=3, but that's as good of a comparison to use as any.

amistre64 · Answer