Question

show that by using definition of sequence Sn=1/2!+1/3!+......+1/n! is cauchy sequence​

Answer 1

Answer:

If 0 <r< 1 and |xn+1 − xn| < rn for all n ∈ N, show that (xn) is a Cauchy sequence. ri−1 = rm − rn 1 − r . Since 0 < r < 1, lim(rn) = 0, and hence (rn) is Cauchy. Therefore, given ϵ > 0, there exists N ∈ N such that for all m, n ≥ N, we have |rm − rn| < ϵ(1 − r).