Talk:1 + 2 + 3 + 4 + ⋯

This page is not a forum for general discussion about 1 + 2 + 3 + 4 + ⋯. Any such comments may be removed or refactored. Please limit discussion to improvement of this article. You may wish to ask factual questions about 1 + 2 + 3 + 4 + ⋯ at the Reference desk.

Archives

1, 2

This page has archives. Sections older than 365 days may be automatically archived by when more than 5 sections are present.

1+2+3+4+5+..........upto infinite = -1/8.[edit]

Let, S=1+2+3+4+5+............. Then, add three digits remaining 1 . I. e. S=1+(2+3+4) +(5+6+7) +(8+9+10) +............... =>S=1+9+18+27+.......... =>S=1+9(1+2+3+4+5+..........) As [1+2+3+4+5+.........=S] Then, S=1+9S. S-9S=1. -8S=1 and S=(-1/8). Hence, proved. Tanuj3301 (talk) 16:19, 14 August 2021 (UTC)[reply]

It is a good idea but answer of this question is -1/8 and also -1/12. As the numbers are going to infinity. So the answer will fluctuate. Tanuj3301 (talk) 16:23, 14 August 2021 (UTC)[reply]

Your transformation is invalid: you may not group terms to sum them. — Vincent Lefèvre (talk) 16:43, 14 August 2021 (UTC)[reply]

You may not not group terms to sum them if the sequence is divergent. If it is convergent, you can. 2A00:1370:8184:9B6:313F:E32F:9192:713E (talk) 14:20, 27 December 2022 (UTC)[reply]

Actually, you need a stronger criteria than convergent to re-arrange terms in a series i.e. you need absolute convergence.

For instance 1 - 1/2 + 1/3 - 1/4 + 1/5 ... converges, but does not converge absolutely. By re-arranging the order of summation, you can make it converge to any number you choose, or make it diverge. Re-arranging the order of summation, or adding series term-by-term is invalid unless the series are absolutely convergent.

By doing these sorts of parlor tricks, you can make a divergent series add up to whatever you want. It might be fun to play around with, but it's not valid math, which is why the Numberphile video got so much criticism. Mr. Swordfish (talk) 14:33, 27 December 2022 (UTC)[reply]

Question[edit]

What can be the application of this equation.... 45.118.159.46 (talk) 15:02, 10 January 2022 (UTC)[reply]

It is an example of a specific value of the Riemann zeta function which has many applications. I don't know how useful this one specific value is (somebody tried to apply it to string theory), but the zeta function itself is quite important. Mr. Swordfish (talk) 14:38, 27 December 2022 (UTC)[reply]