# Sequences and Limits

Not what you're looking for? Search our solutions OR ask your own Custom question.

Consider the real sequence {x_n}_n generated by the iteration scheme

x_n+1 = x_n(2-ax_n), for n = 0, 1, 2, ......

where a>0 and x_0 satisfying 0 < x_0 </= 1/a.

a. Prove 1/a>/=x_n>0 for all n.

b. Prove x_n>/=x_n-1.

c. Conclude that lim n-->infinity x_n exists and determine the limit.

Â© BrainMass Inc. brainmass.com March 4, 2021, 6:55 pm ad1c9bdddfhttps://brainmass.com/math/real-analysis/sequences-limits-70413

#### Solution Preview

Please see the attached file for the complete solution.

Thanks for using BrainMass.

sequence proof

________________________________________

Consider the real sequence {x_n}_n generated by the iteration scheme

x_n+1 = x_n(2-ax_n), ...

#### Solution Summary

Sequences and limits are investigated.

$2.49