## mathew0135 3 years ago Check whether the series defined below is convergent and if so, find its sum.

1. mathew0135

$\sum_{n=1}^{\infty} \frac{ 2^n }{ (-12)^{n-1} }$ and the equation.

2. zordoloom

What math class is this for?

3. etemplin

likely calc 2, because i just had a test on this

4. zordoloom

BTW, this series converges.

5. mathew0135

Math 1B in Australia (presumably similar to calc 2 from what i've seen).

6. zordoloom

ok, the sum will also be -12/5

7. mathew0135

thanks, good to know but how do you work that out?

8. zordoloom

Take the limit as n goes to infinity.

9. mathew0135

thus far i've found the absolute value, then tried to find the limit as it approaches infinity. That's what i believe you do.

10. zordoloom

Ya. That would be correct. So, the form is an+1/an

11. zordoloom

And you plug in the formula that you have into this equation.

12. zordoloom

-(2^n+1)/(12^(n+1)(-1)) all over (2^n)/(-12^(n-1))

13. mathew0135

okay so because the is to a higher power the limit is equal to 0 and thus converges. Hate to ask but how do you find the sum. Think you tried to explain it there but i'm still a bit confused. does: (-(2^n+1)/(12^(n+1)(-1)))/((2^n)/(-12^(n-1))) find me the sum when n=1?