Thread: sum of infinite series

this is for my stats class and i dont have a calc book with me...

the sum of 1/(3^x) where x is from 1 to infinity

thanks

what do a and r represent, and why are they both 1/3 in this case? thanks

a is the first term of the series, and r is the common ratio (the ratio between consecutive terms).

This is a geometric series so you use the formula plato gave to find the sum

ok what if the ratio is 5x/6, is there another formula i can use?

this is for solving the sum of:

x * (1/6) * (5/6)^(x-1)

where x is 1 to infinity

Originally Posted by Plato

does a = x*(1/6) then?

that wont work because then the answer still has an x in it.

Originally Posted by Dubulus

ok what if the ratio is 5x/6, is there another formula i can use? this is for solving the sum of:
x * (1/6) * (5/6)^(x-1) where x is 1 to infinity

To be honest, I cannot say that I really follow what you are trying to do.
Here is an example:

Originally Posted by Dubulus

ok what if the ratio is 5x/6, is there another formula i can use?

this is for solving the sum of:

x * (1/6) * (5/6)^(x-1)

where x is 1 to infinity

The correct formula for this particular sum is .

Originally Posted by icemanfan

The correct formula for this particular sum is .

my problem is that there is an "x" in the sum. this to me means that each new factor in the series isn't changing by a constant ratio.