(c) [5 points] Prove that f(r) [5 p ) = Σ (-1-rn oints Prove that f(x converges uniformly on [-c, c when 0<c<1. lenny
HW: Show that the series __, an n=0 converges whenever ſal < 1, and diverges whenever al > 0.
1 6. Using the power series = Σ c" |x | < 1, find a power series about O for 1 х n=0 1 and state the radius of convergence. (2 - x)2
Soru 2. Suppose the series Ebox" converges for (x1<4. Select all that applies n=0 Yanıtınız: (-1)"b,4" converges n=0 6" M8 M 0,4" converges. n=0 61 6,6"4" diverges. n=0 00 (-1)"b,4" diverges. n=0 boxn+1 n=0 n +1 È converges for all |x<4 nb bmxn-1 converges for |x|<4 n=1 Testi duraklat Geri Sonraki
If s < 1, then Question 1 Not yet answered Not graded Select one: O 1++ + ...= P Flag question 1+8+82 +...= 1++ 32 + ...= O 1+8+82 + ...=
Q2: Find the complex Fourier series (show your steps) - T < x <07 f(x) 0 < x < Q1: Find the Fourier transform for (show your steps) - 1<x< 0 Otherwise (хе f(x) = { 0,
Theory 00 2. Prove that if Vlan] < 1 then an converges. n=1
Exercise 3. Suppose that |2 < 2. Prove that the series converges absolutely.
Show that if G is a group of order np where p is prime and 1 <n<p, then G is not simple.
3m Given the series m=1 4M(3m +5) Σ estimate the error in using the partial sum sg by comparison with the series |- M m=94m Select one: o a. Rg < 0.0000051 b. Rg < 0.000005 C. Rg > 0.0000052 d. R8 < 2.6130051 e. Rg > 0.0000051 (n! For which positive integers k is the series n=1 (kn)! convergent? Select one: a. k< 0 b. k <-6 c. k> 1 O d. k> 0 O e. k > 6