Think about we have a infinite series

summation (j from 0 to infinity) (0.5)^2j=4/3

How did we get this answer?Please help me.

thanks.

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- Jun 17th 2008, 02:16 AMspsInfinite series
Think about we have a infinite series

summation (j from 0 to infinity) (0.5)^2j=4/3

How did we get this answer?Please help me.

thanks. - Jun 17th 2008, 02:20 AMMoo
- Jun 17th 2008, 02:34 AMsps
Thanks Moo

I understood.

I have one more question:

summation (j from 0 to infinity) j*(0.5)^2j=100/225

summation (j from 0 to infinity) j^2*(0.5)^2j=100/135

How did we get those answers? Could you please help me again?

thanks in advance. - Jun 17th 2008, 05:19 AMjjzshen
I can't get line breaks to parse properly on this forum...

There are several ways to do both questions. Here's just an example

View the first one as a geometric series of a geometric series

the second is a little tricker...

Let's try to find a general form for assuming |x| is less than 1

there are probably much easier ways to do this - Jun 17th 2008, 06:14 AMcolby2152
- Jun 17th 2008, 11:58 AMMathstud28