This looks reasonable...

Probability Level 2

Does this holds true for every positive integer n n ? ∑ k = 0 n ( n k ) 3 = ( 3 n − 1 n ) \displaystyle \sum_{k=0}^{n}{n \choose k}^{3}={3n-1 \choose n}

No Yes

X X by X X , 17, Taiwan

This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try refreshing the page, (b) enabling javascript if it is disabled on your browser and, finally, (c) loading the non-javascript version of this page . We're sorry about the hassle.

1 solution

X X
May 2, 2018

Just put in n = 4 n=4 , 346 ≠ 330 346\neq 330

0 Helpful 0 Interesting 0 Brilliant 0 Confused

May I ask then what is the closed-form expression of ∑ k = 0 n ( n k ) 3 \sum\limits_{k=0}^n {n \choose k}^3 ?

Hans Gabriel Daduya - 3 years, 1 month ago

0 pending reports

×

Problem Loading...

Note Loading...

Set Loading...