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