anonymous
  • anonymous
Check whether the series defined below is convergent and if so, find its sum.
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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anonymous
  • anonymous
\[\sum_{n=1}^{\infty} \frac{ 2^n }{ (-12)^{n-1} }\] and the equation.
anonymous
  • anonymous
What math class is this for?
anonymous
  • anonymous
likely calc 2, because i just had a test on this

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anonymous
  • anonymous
BTW, this series converges.
anonymous
  • anonymous
Math 1B in Australia (presumably similar to calc 2 from what i've seen).
anonymous
  • anonymous
ok, the sum will also be -12/5
anonymous
  • anonymous
thanks, good to know but how do you work that out?
anonymous
  • anonymous
Take the limit as n goes to infinity.
anonymous
  • anonymous
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.
anonymous
  • anonymous
Ya. That would be correct. So, the form is an+1/an
anonymous
  • anonymous
And you plug in the formula that you have into this equation.
anonymous
  • anonymous
-(2^n+1)/(12^(n+1)(-1)) all over (2^n)/(-12^(n-1))
anonymous
  • anonymous
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?

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