SOLUTION: can someone show me how to do this??? it says to find the sum of the following infinite series. if a series doesn't have a sum, say "no sum" the problem is 9 - 3 + 1

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Question 93608This question is from textbook
: can someone show me how to do this??? it says to find the sum of the following infinite series. if a series doesn't have a sum, say "no sum"
the problem is 9 - 3 + 1 - 1/3 + 1/9 ......... This question is from textbook

Found 2 solutions by psbhowmick, stanbon:
Answer by psbhowmick(878) (Show Source):
You can put this solution on YOUR website!
This is an infinite Geometric Series with common ratio - (0 < |-| < 1) so this series is converging.
Hence the sum is .
Here a = first term and r = common ratio.

Answer by stanbon(75887) (Show Source):
You can put this solution on YOUR website!
find the sum of the following infinite series. if a series doesn't have a sum, say "no sum"
the problem is 9 - 3 + 1 - 1/3 + 1/9 .........
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You have the sum of two geometric series:
1st series 9, 1/9, 1,81,....
2nd series -3, -1/3, -1/9,....
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Find the sum of each series using S(n)=a[(r^(n+1)-1)/(r-1)
or use what you know about infinite series if you are studying
calculus.
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When you have the sum of each series add them to get the sum
of the given series.
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Cheers,
Stan H.

SOLUTION: can someone show me how to do this??? it says to find the sum of the following infinite series. if a series doesn't have a sum, say "no sum" the problem is 9 - 3 + 1 - 1/3 + 1/9 .