math131Ahw04

# math131Ahw04 - Homework#4 Math 131A Due Feb 11 Spring 2010...

This preview shows pages 1–2. Sign up to view the full content.

This preview has intentionally blurred sections. Sign up to view the full version.

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

Unformatted text preview: Homework #4 Math 131A Due: Feb. 11 Spring 2010 Prof. Maruskin Homework solutions by: Liem Tran. 12.2 Prove that limsup | s n | = 0 if and only if lim s n = 0. Assume limsup | s n | = 0 for n > N , then lim s n = 0 because the absolute values of the supremums reach a limit of 0 which would mean that the sequence s n approached 0 as n , greater than N , increases to infinity. Assume lim s n = 0. For n > N , the absolute value of the limit would approach 0 and as n increases past N then the limit of the supremums would also come to 0. 14.1 Determine which of the following series converges. Justify your answer. (a) ∑ n 4 2 n . a n = n 4 2 n a n +1 a n ⇒ ( n +1) 4 2 n +1 n 4 2 n = ( n + 1) 4 2 n +1 · 2 n n 4 = ( n + 1) 4 2 n 4 = n 4 + 4 n 3 + 6 n 2 + 4 n + 1 2 n 4 = 1 + 4 n + 6 n 2 + 4 n 3 + 1 n 4 2 ⇒ lim 1 + 4 n + 6 n 2 + 4 n 3 + 1 n 4 2 = 1 2 lim a n +1 a n exists so this series converges....
View Full Document

{[ snackBarMessage ]}

### Page1 / 2

math131Ahw04 - Homework#4 Math 131A Due Feb 11 Spring 2010...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online