## 10 points to the person who solves this.

$\sum_0^\infty (-1)^n = ?$

~ by wcuk on August 12, 2008.

### 6 Responses to “10 points to the person who solves this.”

1. 1/2.

it’s some french guy’s summation. i didn’t google it for this round, but i saw it on wikipedia when doing some legwork for a previous puzzle.

1) Completely wrong

3. okay. it’s a divergent series, that’s for sure. so i guess the solution is D.N.E. (DNW?). there’s some crazy french name associated with summations that assigns this equation the value of 1/2. with your permission, i will put up a link to the wikipedia article.

jurkface.

4. Divergent (changing between 0 and 1). We start of with 1-1+1-1+1-1…Thus, all even permutations give a 1 and all odd permutations give a 0. If this were a convergent series, combination would help reach a final answer, but in this example, the inf combined with the negative/positive fluctuation does not allow for convergence and splitting the difference to get 1/2 would be wrong in so many ways unless you said 1/2 +- 1/2 (which is still wrong).

5. Winner winner, chicken dinner.

Jay gets the ten points.

Don, you get no points. Your name dropping and factoids will only get you so far in life. For what it’s worth, this is Grandi’s series

http://en.wikipedia.org/wiki/Grandi%27s_series

and the Cesaro sum is 1/2. Both Grandi and Cesaro were Italian. I look favorably on your mistaken guess of nationality. It shows you did not google the answer.

6. screw you guys, i’m going home