Tessellate S.T.E.M.S. (2019) - Mathematics - Category A (School) - Set 3 - Objective Problem 5

Probability Level 5

Given positive integer n ≥ 100 n \geq 100 , find the value of

∑ i = 0 100 ( 2 n + 1 2 i + 1 ) ( n − i 100 − i ) \sum_{i=0}^{100}\binom{2n+1}{2i+1}\binom{n-i}{100-i}

This problem is a part of Tessellate S.T.E.M.S. (2019)

2 201 ( n + 99 ) ! ( 2 n + 1 ) 201 ! ( n − 100 ) ! \frac{2^{201}(n+99)!(2n+1)}{201! (n-100)!} 2 200 ( n + 100 ) ! ( 2 n + 1 ) 201 ! ( n − 100 ) ! \frac{2^{200}(n+100)!(2n+1)}{201! (n-100)!} 2 202 ( n + 100 ) ! ( 2 n + 1 ) 201 ! ( n − 99 ) ! \frac{2^{202}(n+100)!(2n+1)}{201! (n-99)!} 2 201 ( n + 100 ) ! ( 2 n + 1 ) 201 ! ( n − 100 ) ! \frac{2^{201}(n+100)!(2n+1)}{201! (n-100)!}

Tessellate S.T.E.M.S. Mathematics by Tessellate S.T.E.M.S. Ma… , 26

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1 solution

Monu Kumar
Nov 22, 2018

Given n=100 will satisfy this so I Just put n=100 and checked the options

0 Helpful 2 Interesting 0 Brilliant 0 Confused

This can be proved by using snake oil method. It is a powerful technique for proving combinatorial identities.

Srikanth Tupurani - 2 years, 6 months ago

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