0
$\begingroup$

If we let $f_n(x)=\frac{x^2+nx}{n}$ for $x\in R$. I am trying to show that we can make $f_n$ converge uniformly on the interval $[R,-R]$ For any fixed $R\in(0,\infty)$

One way to show uniform convergence is using the M-test.

So I need to find a series M such that $\sum f_n<=M$ and then if the series $\sum M$ converges then $\sum f_n$ must converge.

But how can I find that series $\sum M$ and then apply the M test.

  • 0
    I don't get it: Weierstrass M-test if for **series** of functions, and you have here a *sequence* of functions... – 2017-02-17
  • 0
    Again: you have, as in your other 2-3 questions, a **sequence** of functions which you wanted to prove something about their (The sequence!) converging pointwise, uniformly, etc. to some function. Now you want to use the M-test, but this is for **series of functions**, not *sequences of functions* ! – 2017-02-17
  • 0
    okay I understand, so I must use similar logic as before – 2017-02-17

0 Answers 0