anonymous
  • anonymous
how do you find the sum from n=1 to infinity of n(1/4)^(n-1)
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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perl
  • perl
did you try using the ratio test
anonymous
  • anonymous
I thought the ratio test tells you if it is convergent or divergent not what the actual sum is. By the ratio test it is convergent.
perl
  • perl
|dw:1353738999087:dw|

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More answers

perl
  • perl
is that the question>
anonymous
  • anonymous
yes
perl
  • perl
the expression inside looks close to the derivative of 1/4 ^n-1
perl
  • perl
the answer is 16/9
anonymous
  • anonymous
how did you get that?
perl
  • perl
lets look at the partial sums
perl
  • perl
take the sum from n=1 to m
anonymous
  • anonymous
16/9
perl
  • perl
do you have a justification
anonymous
  • anonymous
|dw:1353747498242:dw|
anonymous
  • anonymous
derivative
anonymous
  • anonymous
x=1/4
anonymous
  • anonymous
|dw:1353747595344:dw|
perl
  • perl
what about the limits ?
anonymous
  • anonymous
not needed
perl
  • perl
i could start the second limit at n = 2
anonymous
  • anonymous
how did you get 1/(1-x)^2 from the step above?
anonymous
  • anonymous
|dw:1353747789535:dw|
anonymous
  • anonymous
take the derivative both sides
anonymous
  • anonymous
ok. cool. thank you
anonymous
  • anonymous
(:
anonymous
  • anonymous
you can also take integral sometimes..
perl
  • perl
that formula is incorrect
perl
  • perl
|dw:1353740583496:dw|
perl
  • perl
|dw:1353740607290:dw|
perl
  • perl
very sloppy indeed
anonymous
  • anonymous
http://mathworld.wolfram.com/GeometricSeries.html
anonymous
  • anonymous
I did not notice your series start from 1, answer will be (16/9)-1
anonymous
  • anonymous
|dw:1353748518528:dw|
perl
  • perl
the answer is correct , it is 16/9
perl
  • perl
|dw:1353741295190:dw|
perl
  • perl
the first term is zero, so we can ignore it
anonymous
  • anonymous
the original solution was correct. the left hand side is defined at n=1, the RHS doesn't have to be defined at 1 because its the formula for the sum of geometric series i.e. r=x.
perl
  • perl
|dw:1353741624657:dw|

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