sheet2 - contain sentences explaining what you are doing...

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

View Full Document Right Arrow Icon
CM221A ANALYSIS I Exercise Sheet 2 1. Is the following statement correct: if lim n →∞ a n = 1 then lim n →∞ ( na n ) = n ? 2. Find lim n →∞ (sin n ) 2 - n . 3. Evaluate lim n →∞ ± n + 1 - n ² . Hint: use x 2 - y 2 = ( x + y )( x - y ). 4. Find lim n →∞ c 2 n - 1 c 2 n + 1 ! for all real values of c . Look separately at | c | > 1 , | c | < 1 and | c | = 1. 5. Find out which of the following series converge. Your solutions must
Background image of page 1
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: contain sentences explaining what you are doing and what tests you are using. (i) X n =1 2 n-n 3 n + n 2 (ii) X n =1 n n n ! (iii) X n =1 (-1) n n k 1 + 2 n (iv) X n =0 ( n-1) ( x + 1) n ( n + 1) 2 n (consider all possible values of x R ). 1...
View Full Document

This document was uploaded on 01/31/2011.

Ask a homework question - tutors are online