Thread: series problem

does this converge or diverge, if it converges, to what sum.

(2/3) - (4/9) + (8/27) - (16/81)

so a(n) = (-1)^n * 2^(n+1)/3^(n+1)

i know its convergent by alternating series test, but how can i figure out what sum it converges to without Sn formula?

Originally Posted by synnexster

does this converge or diverge, if it converges, to what sum.

(2/3) - (4/9) + (8/27) - (16/81)

so a(n) = (-1)^n * 2^(n+1)/3^(n+1)

i know its convergent by alternating series test, but how can i figure out what sum it converges to without Sn formula?

It is a geometric series,
The ratio is,
-2/3
Which is convergent since,
|-2/3|<1
Now just use the infinite geometric sum formula to find the sum.

so the sum would be a/(1-r) right?
so (2/3)/(1-(2/3)) = 2

Originally Posted by synnexster

so the sum would be a/(1-r) right?
so (2/3)/(1-(2/3)) = 2

Indeed, I shall wager my soul for that!