/sci/ - Science & Math » Thread #11404883

7KiB, 565x240, sum.png

View Same Google iqdb SauceNAO

Upper bound for sum of binomial coefficients

Anonymous Fri 21 Feb 16:04:31 2020 No.11404883 View Reply Original Report

Quoted By: >>11405104 >>11405485

Hey, sci, is there an upper bound / approximation for the sum of the first k binomial coefficients of order n. k <= n/2

Anonymous

Anonymous Fri 21 Feb 2020 16:18:48 No.11404904 Report

Quoted By: >>11405066 >>11405105

$\sum_{t=1}^k {n \choose t} \leq k \cdot 2^n$

Anonymous

Anonymous Fri 21 Feb 2020 17:31:56 No.11405066 Report

Quoted By:

>>11404904
I meant something useful.

Anonymous

Anonymous Fri 21 Feb 2020 17:39:53 No.11405104 Report

Quoted By: >>11405110 >>11405113

>>11404883
The sum is equal to n+1 choose k+1

Anonymous

Anonymous Fri 21 Feb 2020 17:40:04 No.11405105 Report

Quoted By: >>11405113

>>11404904
I meant something useful.

Anonymous

Anonymous Fri 21 Feb 2020 17:41:06 No.11405110 Report

Quoted By: >>11405116 >>11405134

>>11405104
Why would that be?

Anonymous

Anonymous Fri 21 Feb 2020 17:42:09 No.11405113 Report

Quoted By:

>>11405104
Why would that be the case?

>>11405105
Ops sorry for the double post, my browser bugged.

Anonymous

Anonymous Fri 21 Feb 2020 17:42:43 No.11405116 Report

Quoted By: >>11405134

>>11405110
There is double counting argument to prove it. Give me a few mins I will remember it.

Anonymous

Anonymous Fri 21 Feb 2020 17:48:32 No.11405134 Report

Quoted By:

>>11405110
>>11405116
Sorry, fuck me, it is the sum over the upper argument of the coeficient, that gives that.

Anonymous

Anonymous Fri 21 Feb 2020 20:07:35 No.11405485 Report

Quoted By:

>>11404883
The sum equals 2^(n-1) if n is odd (It's exactly half of all the binary strings of size n you could make).

Anonymous

View Same Google iqdb SauceNAO 77c5d4ffb9961aa34a889cfc488d5950.png, 2MiB, 960x1198

Anonymous Fri 21 Feb 2020 20:58:23 No.11405593 Report

Quoted By:

Hello. my dear mathematicians!
Does anyone have please good scan of "Concrete Mathematics: A Foundation for Computer Science"?

Capcode	All Only User Posts Only Moderator Posts Only Admin Posts Only Developer Posts
Show Posts	All Only With Images Only Without Images
Deleted Posts	All Only Deleted Posts Only Non-Deleted Posts
Ghost Posts	All Only Ghost Posts Only Non-Ghost Posts
Post Type	All Only Sticky Threads Only Opening Posts Only Reply Posts
Results	All Grouped By Threads
Order	Latest Posts First Oldest Posts First

Your latest searches