100 4. If En=1 an converges absolutely, then n=1 an converges conditionally (C). 1 For p > 1, the root test applied to Ln=1 n is inconclusive (C). 5.

9. For the convergent series E0 find an upper bound for the error |S – S3]. Show work. n4

I’m stuck on these 2 hw problems. Thank you

Suppose {fn}n=1 converges uniformly on E. Show {fn=1 converges pointwise on E.

help me #25

6.2.2

10.4. #2 a.) Please help ty.

2. (25.10) xn (a) Show Σ 1n converges for x € [0, 1). E 1+xn (b) Show that the series converges uniformly on [0, a] for each a with 0 < a < 1. (c) Does the series converge uniformly on [0, 1)? Explain.

(4) Suppose {a„}1 converges to L and that a, 2 0 for all n. Prove that {Van}1 converges to L. Tip: Note that by problem (2), L > 0. For the case L = 0, you can just cite the previous problem. Finally, for the case L > 0, use (Van – VL)(yan + VL) = a, – L to deduce that n=1 lan – L. IVan – VI| < VL