Section10.1-Sequences

Anotherexample sin2 n

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: cannot be applied to a sequence, but can be applied to the corresponding continuous function. Another Example sin(2 n) Is the sequence, , convergent or divergent? Solution: lim sin(2 x) x does not exist, but lim sin(2 n) 0 , so the sequence is convergent. n Theorem 2 lim a 0 If , then lim a n n n n 0 Examples n 1 1 Does the sequence, , converge or n diverge? Solution: 1 n 11 nn 1 n1 0, so lim 1 0 n n n n lim n1 1 converges to 0 n Example r For what values of r does converge? n Solution: 0 for 0 r 1 lim r x 1 for r 1 x for r 1 SO 0 for 0 r 1 convergent n lim r 1 for r 1 convergent n for r 1 divergent Note that rx is defined only for r > 0. What about r ≤ 0 ? Example ‐ continued lim r n 0 if r 1 n lim r n does not exist if r 1 n For example 1 n 1 1 1 1 , , , ,... 2 2 4 8 16 1 1,1, 1,1,... n 2 2, 4, 8,16,... convergent divergent n divergent Summary For {rn} r n r n converges to 0 for 1 r 1 converges to 1 for r = 1 r n diverges otherwise Try It 1 p n For what values of p does converge? Try It...
View Full Document

This note was uploaded on 02/24/2014 for the course APMA 1110 taught by Professor Morris during the Fall '11 term at UVA.

Ask a homework question - tutors are online