Question Number 103410 by Ar Brandon last updated on 14/Jul/20

Σ_(k=0) ^n (((−1)^k )/(k!))=?

Answered by mathmax by abdo last updated on 15/Jul/20

we have e^(−1)  =Σ_(k=0) ^∞  (((−1)^k )/(k!)) =Σ_(k=0) ^n  (((−1)^k )/(k!)) +Σ_(k=n+1) ^∞  (((−1)^k )/(k!))  =Σ_(k=0) ^n  (((−1)^k )/(k!)) +R_n    ( rest at the serie of taylor) ⇒  Σ_(k=0) ^n  (((−1)^k )/(k!)) =(1/e)−R_n    with lim_(n→+∞)  R_n =0