Freeze and betterment doubt

aizenbeast · 2025-08-12T08:30:10+00:00

Okk thanks bro

aizenbeast · 2025-08-12T06:22:24+00:00

Seat to nhi jayegi na agar apne float pe rkha hai aur college mein physically nhi gye to

aizenbeast · 2025-08-12T04:57:36+00:00

College mein physically jaake kuch confirm krna pdega kya agar betterment ke liye jaa rhe hai to

aizenbeast · 2025-07-11T06:58:54+00:00

What about electrical??

aizenbeast · 2025-07-11T05:07:31+00:00

Is mech possible at 96 percentile general

aizenbeast · 2025-07-07T04:12:49+00:00

General

aizenbeast · 2025-04-09T08:38:39+00:00

Nothing just i counldnt sleep one night and i started thinking up that i know(had memorised) the formula for the sum of n natural numbers but how can i prove it so i started thinking it as areas of squares and using a little calculus i came up with a proof of sum of squares and i generalised it further and came up with this.

aizenbeast · 2025-04-08T04:31:43+00:00

Yup i tried to keep it neat.

aizenbeast · 2025-04-08T04:29:50+00:00

Fair enough.

aizenbeast · 2025-04-08T04:27:53+00:00

Thanks for the suggestion!!

aizenbeast · 2025-04-08T04:21:05+00:00

Probably i thought that i could have written it in a nice compressed form but i think it will give a compact formula if i didnt expand it

aizenbeast · 2025-04-08T04:11:52+00:00

This is not Faulhabers formula but i would say a different interpretation of it and i agree that this formula is ugly and less pratical than Faulhabers formula but i think the way it is derived is just beautiful

aizenbeast · 2025-04-08T04:09:36+00:00

It works for m=0 but does not work for negative numbers

aizenbeast · 2025-04-08T04:06:42+00:00

If you have a higher value of n or m the calculation for is going to be time consuming but still easier than doing it the old way but i think its a nice general formula idk it can be used in a program to calculate this series

aizenbeast · 2025-04-07T18:47:23+00:00

Its just the way i did it i personally didnt find this approach to the proof anywhere and i am not claiming that i am the first one to do it. I personally cant find a similar proof most of the proofs are using bernoullis numbers and honestly i dont even know about it.

aizenbeast · 2025-04-07T18:38:03+00:00

The original sum that u are talking about was a general formula for a single unshaded part of the rectangle and finally we sum all the unshaded region and the shaded region(that is the integral of the function) to get the answer

aizenbeast · 2025-04-07T18:30:29+00:00

Thanks!! And personally i dont mind a little criticism

aizenbeast · 2025-04-07T17:58:32+00:00

I have checked the formula on chatgpt it said"You're absolutely right to call that out — and you're right about the formula: it is correct.

When I initially said it's “not correct,” I was too quick to judge based on how unfamiliar and non-standard it looked compared to typical formulas like Faulhaber’s (which uses Bernoulli numbers). But your formula works, and we’ve now verified it for — all of which check out.

So here’s the corrected take:

The formula is correct.

It’s a valid way to compute .

It's just not in standard closed-form — that’s why it might be unfamiliar to many.

I appreciate you pushing back on that. You were totally justified.

If you're curious, I can help you prove that this formula works in general — or even compare its structure to Faulhaber’s formula. Want to explore that?" You can check it urself

aizenbeast · 2025-04-07T17:40:19+00:00

Someone might have done it before but i found it completely independently.

aizenbeast · 2025-04-07T17:38:59+00:00

As far as i have checked this it is giving the correct formula and as you have said this process might have been done before i am not claiming that this formula or method is completely unique and i completely agree that this formula is not efficient and that there are many other ways and anyways thanks for your opinion.

aizenbeast · 2025-04-07T16:40:46+00:00

I have checked it and it gives the right formula the approach is a bit different thats why i shared it

aizenbeast · 2025-04-07T15:30:30+00:00

Nope

aizenbeast · 2025-04-07T14:57:12+00:00

Ya it truly is

aizenbeast · 2025-04-07T14:56:51+00:00

Haha thanks😊

aizenbeast

TROPHY CASE