Thread: Geometric series

Express the decimal as an rational number through geometric series

1.213213213....



I understand how to do say .2222222222

as

With my A = 2/10

and my r = 1/10

Any help would be appreciated! Im sure its me just brain farting, I cant seem to put it together.

Here is a hint to get you started.

Originally Posted by Plato

Here is a hint to get you started.

Hm still lost but i did manage to fudge an answer Algerbraically though not entirely correct

by using An = 1.213213213

then multiplying both sides by 100

100An = 121.3213213

then subtracting them and eventually getting

Originally Posted by Plato

Thanks! I was not paying attention to the n=1 on the summation where on geometric series it doesn't effect the convergence/divergence just the value. Failing to realize that n=0 was my downfall. Case in point many thanks.