Question

- (4 points) Determine the following limit lim en n-> if the sequence is defined by Xo = 4, and for n = 1,2,3,... 9xn-1 -5 In = In-1- 4xn-1-9 2x2 'n-1

Answer 1

The sequence is defined by and for n=1,2,3,.. 2x -geeni den - 5 and 42n-1 na 1 2x² - 9nxo 5 4 47o -9 4 - 2016 - 944-S 16-9 = 4- = 4 + 3 1 2 = 5+23 for na 2 2xt-ga-s 22 4 424-9 37 7 2*(3,772 9237 7 4*34 9 11 37 7 162 595 5 8 595 8 25+ 595 This shears that nen > 5 for all n), 1 Avso xenti < Rn for an a>, 1: there bere the sequence {en} to monotonic decreasing let lim xn=d. We have 2 2 ani xn-e gans limit as nad 4Run we have proceeding to l=e 2 e-91-5 48-9 24-91-5=0 a 24-10878-5=0 Q 2.2(4-5)+1(8-5)=0 a (1-5)(2d+1)=0 either f-5=0 o 24+10 Pre-5 ods-2 since enxo for unen is not possible there fore the limit of the sequence lim xn=5 is 5 Thus no