Find the sum of series (1 Viewer)

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Can anyone teach me how to find the sum of the series in terms of n in the following:

1+2x3^2+3x3^4+............+(n+1)3^2n

Thx!
 

0rthodontist

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This can be done with generating functions if you know them.
1. Find the generating function for 1, 3^2, 3^4, ...
2. From this, find the generating function for 1, 2*3^2, ...
3. Find the generating function for (n+2)*3^(2(n+1)), (n+3)*3^(2(n+2)), ...
4. Subtract the latter from the former and evaluate at 1.
 
0rthodontist said:
This can be done with generating functions if you know them.
1. Find the generating function for 1, 3^2, 3^4, ...
2. From this, find the generating function for 1, 2*3^2, ...
3. Find the generating function for (n+2)*3^(2(n+1)), (n+3)*3^(2(n+2)), ...
4. Subtract the latter from the former and evaluate at 1.


i dont know what generating function is but what i know is to use the summation sign to do this kind of question. i still cant do it.........
 

shmoe

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Homework Helper
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You might find it easier to try and sum:

[tex]1+2x^2+3x^4+\ldots+(n+1)x^{2n}[/tex]
 

shmoe

Science Advisor
Homework Helper
1,993
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You might find it easier to try and sum:

[tex]1+2x^2+3x^4+\ldots+(n+1)x^{2n}[/tex]

It's not quite a geometric series, but can you turn it into one?
 

0rthodontist

Science Advisor
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Okay--what sums can you do that might be relevant?
 
shmoe said:
You might find it easier to try and sum:

[tex]1+2x^2+3x^4+\ldots+(n+1)x^{2n}[/tex]

It's not quite a geometric series, but can you turn it into one?

i just can do till this step:

n+1 E(Sigma) r=1 (r*x^(r-1))
 
0rthodontist said:
Okay--what sums can you do that might be relevant?


I can do the summation of x, x^2 .....x^n, x(x+1),x(x+1)(x+2).....

actually this is my first time to touch this kind of math:)
 

0rthodontist

Science Advisor
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Well--
x + x^2 + ... + x^n
Take the derivative with respect to x, both term-by-term and in the sum you know.
 
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