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- Thread starter jacks
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- Feb 9, 2012

- 118

Take a look at $f(n,m).$

- Jan 26, 2012

- 890

Might I ask where this question comes from?Let $f(m,n) = 3m+n+(m+n)^2.$ Then value of $\displaystyle \sum_{n=0}^{\infty}\;\; \sum_{m=0}^{\infty}2^{-f(m,n)}=$

The sum converges very quickly and can be evaluated numerically with 4 terms of each summation (it is \(\approx 1.33333\), which is very suggestive ... ) to good accuracy.

CB

(why the previous calc got the wrong answer I still have no idea)

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- #4

- Feb 7, 2012

- 2,708

$$\begin{array}{cc}&\;\;\;\;n \\ \rlap{m} & \begin{array}{c|cccc} &0&1&2&3 \\ \hline 0&0&2&6&12 \\ 1&4&8&14&. \\ 2&10&16&.&. \\ 3&18&.&.&. \end{array} \end{array}$$

Doesn't that suggest something very interesting about the range of the function $f(m,n)$?

- Feb 9, 2012

- 118

It's from a Putnam. I don't remember the year though.Might I ask where this question comes from?