Question

6. (1 point) Prove that if (an+ba) diverges. bn diverges, then an converges and nel KSB: 0MFA CIN 8. (1 point) Find the total length of the zigzag path. Note that each bounce meets a side at a right angle and bounces off at a 30° angle. 30% L

Answer 1

let , The su be series of too can oriten Co an Cantbn Z Car br Z Cantbn 1 bo direrges given that have we diFferen ce behdee, too series olirerges of the two serjeg must diverges as then one herce is EAn IS convexges but divenges L antbr)

The to tal lena th of is L +LIL2+ Lat- L NOus, Consider tte 80 First triarle we have, sin Q こ OPposi te side LI L tApotenuse L 31C30) L L 2 for seeond tiagle Le E sincao) L sin 30 L2 LI 2 L し2 ニ L 4 uave get, Di appooao m L we Sae Ln - ( 1 2. Zag patb is しり Thus length of のニ 2

Lの (にu . LotLitし2t L 2. This is aeomeaic eeries, cohore, i (2) L pub Lo 9D- Lo Land L 2 uwin Fermula, Sto se L L 112 1 Lo 2 L l 12 Tota) leoath of 2 L