How Do I Find the Nth Term and Sum of These Series?

[wccrooks]

Ok i have a few here that i have no idea what to do
b]1. Homework Statement [/b]

Find the nth term in the series
1/2, 1/3, 2/9, 4/27, 8/81, 16/243

also

\Sigma (-1)^n-1/ 5n+1
find the sum
Urgent help neededdd ahha.. Thanks

 

[jhicks]

For the first: Try to express the terms as a product of powers of 2 and 3. Biggest hint: 1/2=2^(-1)*3^0. For the second, could you clarify the sum?

 

[wccrooks]

So the 1/2 is just clarifying an alternating series? I am completely lost on that problem. for the second i don't know what you mean either haha... all i know right now is it is an alternating problem... I have been trying to do these for like 3 hours to no success haha..



edit---
Well thanks for the first part i figured out the nth term. I am just super slow haha... The second problem however the only info i have oin it is its starts at n=1 the the (-1)^n-1/5n+1 then it asks me to find the sum I am pretty sure that all i have

 

[jhicks]

Like I said, clarify the sum. Use parentheses and such because I can't make any sense out of what you wrote.

 

[zzoon]

The sequence looks like 2^(n-1) * 3^n starting from 0

 

[wccrooks]

ok starting at n=1 ((-1)^n-1)/(5n+1) so as far as i got is the (-1)^n-1 is pulled out as alternating leaving 1/(5n+1) and they want the sum of that