Question

prove that Sn = 1/1! + 1/2! + ... + 1/n! is a contractive sequence prove that Sn = 1/1! + 1/2! + ... + 1/n! is a contractive sequence @Mathematics

Answer 1

so man this is over my head

Answer 2

sorry*

Answer 3

np, thank for looking

Answer 4

Sn = 1/1! + 1/2! + ... + 1/n!
Sn = 1 + 1/2 + 1/6 + 1/24 + 1/120 + 1/720 + ..............+1/n!
as u can see that the denominator is increasing so the value of the first term is the highest it is decresing along the sequence so this sequence is a contractive one !

Answer 5

it's not a proof, proving as |Sn+2 - Sn+1| <= K|Sn+1 - Sn|

Answer 6

hahahaha................

Answer 7

0 < K < 1

Answer 8

Sn+1-Sn = 1/(n+1)!
Sn+2 - Sn+1 = 1/(n+2)!

now just plug in n= 1in the above two equations u will get
Sn+1-Sn = 1/(1+1)! = 1/2! = 1/2 = 0.5
Sn+2 - Sn+1 = 1/(1+2)! = 1/3! = 1/6 = 0.16666

so\[\S_{n+2} - \S_{n+1} \le \S_{n+1} - \S_{n}\]

Answer 9

it's still not a proof, it;s algebra

Answer 10

oh ok. ya I will do that

Answer 11

thanks