A Binomial Coefficient Sum: ∑ m = 0 n ( − 1 ) n − m ( n m ) ( m − 1 l )

Question

A Binomial Coefficient Sum:       ∑          m      =      0              n        (  −  1      )          n      −      m                          (                    n      m                      )                                (                            m        −        1            l                      )

Kylan Simon · Accepted Answer

∑          m      =      0        n    (  −  1      )          n      −      m                          (                    n      m                      )                                (                            m        −        1            l                      )              =  (  −  1      )          l      +      n        +      ∑          l      +      1      ≤      m      ≤      n        (  −  1      )          n      −      m                          (                    n      m                      )                                (                            m        −        1            l                      )            So we need to compute this last sum. It is clearly zero if   l  ≥  n, so we assume l

A Binomial Coefficient Sum: <munderover> ∑ <mrow class="MJX-TeXAtom-O

Answered question

Answer & Explanation

New Questions in Electric current