Question

Check whether the series defined below is convergent and if so, find its sum.

Answer 1

\[\sum_{n=1}^{\infty} \frac{ 2^n }{ (-12)^{n-1} }\]

and the equation.

Answer 2

What math class is this for?

Answer 3

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

Answer 4

BTW, this series converges.

Answer 5

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

Answer 6

ok, the sum will also be -12/5

Answer 7

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

Answer 8

Take the limit as n goes to infinity.

Answer 9

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.

Answer 10

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

Answer 11

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

Answer 12

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

Answer 13

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?