An Infinite Divergent Series

Algebra Level 3

What is the Ramanujan summation of $\displaystyle \sum_{k=1}^{\infty} k$

-\frac{1}{12}

\pi

0 Divergent

1 solution

Snehal Shekatkar
Feb 21, 2014

Of course I am not discouraging you from posting problems of course but still I would really like to discourage you guys from posting such problems. There are two reasons involved. First, the question is rather of informative type and if one already has read something somewhere then without any effort he can "solve" this. Thus we are being unfair to those who used their logic to come up with infinity as the answer (but never heard of -1/12). Second reason is that the actual argument involved in showing that this sum has "value" -1/12 is extremely involved and someone who solved it may not at all be able to understand the argument.

Thanks and Happy problem solving! :)

I really don't see anything wrong with the question. I specifically asked for the Ramanujan summation in the question. Ramanujan summation was the key word and its hard not to notice, so when people answered divergent they did so without truly knowing what the question was asking. I know David Mattingly and Aaron Kau post quite a lot of informative type questions and no one seems to have a problem with those problems. For example check out this problem: Squirrel Problem . Not many people probably know the answer to this question immediately but it is a fun question to ask. If you don't want to lose rating points don't answer the questions blindly. I don't care too much about my rating so I answered the question for the fun of it and I got it wrong. I'm not going to go complain to Dave Mattingly that I didn't have the logic to answer it. If I didn't have the logic to answer the question and I didn't want my rating to go down I shouldn't have answered it.

Cole Coupland - 7 years, 3 months ago

you are right man, these type of questions ,ratings aside, increase our knowledge. Anyway, if the answer were so straightforward, why would someone post it ? These type of questions should be ENCOURAGED instead of being discouraged as they keep aside the competition thing an their goal is to increase the knowledge of anyone who spots them. For eg., I didn't know what the answer was and just guessed, and when it turned out to be right, I went all around the internet and now i have more knowledge than i had before this question.

Aakarshit Uppal - 7 years, 3 months ago

I think this would be my last reply to this thread. Just because you want to compare Squirrel problem with this one, try giving explanation of this sum being equal to -1/12 in similar way David explained how squirrels can use their tails to balance themselves. Let us say that you have 3 full days to write the solution. Answer should be such that people will understand it just like they understood David's solution. Goodluck! :)

Snehal Shekatkar - 7 years, 3 months ago

Here you go : Video Proof

Aakarshit Uppal - 7 years, 3 months ago

This wasn't meant to be a question where a rigorous process was involved as it was based on whether you know it or not. Here's another one of Dave's problems link . Part of the answer can be seen using The Falling Cat Problem which is quite rigorous to show, but the nature of the problem isn't about gaining a full * understanding * of the mechanism but rather gain an * appreciation * of the mechanism. These are two very different things. The intention I had in making this problem was giving people the * appreciation * that divergent series can be summed using Ramanujan summations. My intention was not trying to be unfair to people who didn't know about this form of summation. I don't need to make a solution to justify myself as this is simply about knowing the answer and/or teaching yourself about the concept of summing a divergent series if you didn't know the answer at first. 69% of people solved it so it didn't seem to be an issue at all and as Aakarshit uppal said, it's better to learn new things then to be overly concerned about ratings and why a question is unfair. He now has an appreciation that divergent series can be summed using certain methods and that's what counts.

Cole Coupland - 7 years, 3 months ago

I did not know this!!!

A Brilliant Member - 7 years, 3 months ago

You mean you got it wrong.. thats what I am saying..

Snehal Shekatkar - 7 years, 3 months ago

But at least now he knows it and that is something good.

Aakarshit Uppal - 7 years, 3 months ago

An Infinite Divergent Series

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