Sum of (i^2)/(4^i)

1. Jun 21, 2004

Johnny Leong

Sum of (i^2)/(4^i) where i is from 0 to infinity.

2. Jun 21, 2004

turin

If you just want an approximate answer, then consider the convergence of the series.

3. Jun 21, 2004

Johnny Leong

Sum of (i^2)/(4^i) > 1/4 + 1/4 + 9/16 + Sum of 1/(4^i) where 4<=i<=infinity.
Can this be a good approximation?

4. Jun 21, 2004

HallsofIvy

Staff Emeritus
Well, that was what you were told when you posted this under "k-12 homework".

5. Jun 27, 2004

turin

The sequence of partial sums is monotonic, so you definitely know that the infinite series must be greater than any partial series. Then, you know that any number greater than 1 is greater than 1, so that remaining sum also fits the bill.

I actually worked this summation out to about 20 terms, and it appears as though it is a recognizable fraction.

6. Jun 27, 2004

7. Jun 27, 2004

turin

8. Jun 28, 2004

I had no trouble following it and I'm just out of high school.

Alternatively, do you know of another, less advanced way of solving it? I'd be interested in seeing it.

9. Jun 28, 2004

arildno

So would I!
Perhaps I shot a sparrow with a cannon..

10. Jun 28, 2004

turin

Add about twenty of the terms. You can definitely see the series converge. This is "less advanced" (and more straightforward). Though I certainly admit that it does not smack of the elegance provided by arildno.

I would say you fought an armored knight with a rapier.