Exercise 6.4.1

Question

Supply the details for the proof of the Weierstrass M-Test (Corollary 6.4.5).

Ulisse Mini · Accepted Answer

Let $\epsilon > 0$. Since $\sum^\infty_{n=1}M_n$ converges, by the Cauchy Criterion for Series there must be some $N$ where if $n>m > N$ then $\sum^{n}_{i=m+1}M_i < \epsilon$. Then $$\left|\sum^n_{i=m+1}f_i(x)\right| \leq \sum^n_{i=m+1}\left|f_i(x)\right| \leq \sum^n_{i=m+1} M_i < \epsilon$$ and applying the Cauchy Criterion, the proof is done.

Exercise 6.4.1

Answers

Comments

Exercise 6.4.1

Answers

Comments

Add answer