Question

8 W 1 n= 7+1 SH Prove disprove Converge or diverge defination. ch#2 fin) = f Sin (1) ocxel prove disprove the Graph of f has content o

Answer 1

o series is Convergent iff sequence of its partial Sum is convergent be given - given series Let s ntl n=1 K and up be "x= sequence of its its partial sum . ntl n=1 Cauchy sequence А sequence {uny is said to be cauchy if I tor any Exo I pra na nGIN lup Untp unl Le A real sequence is convergent iff it is cauchy ( If a sequence is not cauchy then it is not convergent

k Suppose 4k = 9 is conve cauchy ntl v=1 PEIN Such that Uptp - Ykke for Ero any

let k=p - Чур – Vk - Чер - ЧР Чар Чр 1. +... + 7 + ) P+) Pt2 г 3 P+P 1 | — -- P4/ 11... + 2P Pt2 Pt — т... + Up UP Pti <P+P 7 pti 2P Р Р 2P L 4 ЧЕХР че | >, і} we choose E= 1/4 upl ke then ТЧ 4р - : 11

{n} is is not Cauchy {n} not convergent. is not convergent. n+ n=1