anonymous
  • anonymous
Find the sum of the following infinite geometric series if it exists 1/2 + -1/4 + 1/8 + -1/16
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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schrodinger
  • schrodinger
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anonymous
  • anonymous
We have x/y^2 . OK ?!
anonymous
  • anonymous
But in each 2th we have (-) too !
anonymous
  • anonymous
I know the common ratio is -1/2

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anonymous
  • anonymous
So what do you want ?!!!
anonymous
  • anonymous
the sum of it
anonymous
  • anonymous
In an arithmetic series I can find the sum of that but is there a formula for finding the sum of a geometric series?
anonymous
  • anonymous
-0/1
anonymous
  • anonymous
What does that mean?
anonymous
  • anonymous
YES ! LOOK :
anonymous
  • anonymous
?....
anonymous
  • anonymous
Number.(end.first)/2
anonymous
  • anonymous
how do you find the last number?
anonymous
  • anonymous
You have it ! You want a way to find the sum .HA? It s a way to find that .!
anonymous
  • anonymous
There is no last number if it's infinite?
anonymous
  • anonymous
I thought I was suppose to use sigma somehow?
anonymous
  • anonymous
You want nth ? OK ?
anonymous
  • anonymous
What?
anonymous
  • anonymous
I just want to find the sum of the infinite geometric series if it's possible? -.-
anonymous
  • anonymous
and I don't know how to
anonymous
  • anonymous
I don't understand what you are trying do..
anonymous
  • anonymous
In this you want to find the n th Number . Right ?
anonymous
  • anonymous
what is the nth number?
anonymous
  • anonymous
Amm for example when we say 2th day ... It s n th Number !
anonymous
  • anonymous
No i dont want the nth number i want the sum of the entire infinite series..
anonymous
  • anonymous
I can get the nth number but it asks for no nth number.
anonymous
  • anonymous
it asks for the entire sum of the infinite geometric series.
anonymous
  • anonymous
for a GP with first term 'a' and common ratio r less than 1 the sum for infinite terms is\[\frac{ a }{ 1-r } = S_n\] it is derived from applying the infinite limit to the formula for the sum of n terms.
anonymous
  • anonymous
how do you get the sum of infinite terms?
anonymous
  • anonymous
Does that equation equal the sum?..
anonymous
  • anonymous
yes S_n is the sum of the infinite GP
anonymous
  • anonymous
Then would it be 1/3?..
anonymous
  • anonymous
Correct, the sum is \[\frac{ 1/2 }{ 1-(-1/2) } = \frac{1/2}{3/2}= \frac{1}{3}\]
anonymous
  • anonymous
Okay. Thanks.

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