M147A2

# M147A2 - MATH 147 Assignment#2 Due Friday October 9 1 For...

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

MATH 147 Assignment #2 Due: Friday, October 9 1) For each of the following sequences determine if it converges or diverges. If it converges ﬁnd the limit: a) { n n +1 } b) { sin( n ) n } c) { n + 1 - n } d) e n n ! e) { n cos( ) 2 n +1 } 2) We will later be able to show that 1 n + 1 < ln( n + 1) - ln( n ) < 1 n a) Let a n = 1 + 1 2 + 1 3 + ··· + 1 n - ln( n ). Prove that { a n } converges. Note: γ = lim n →∞ a n is called Euler’s constant. It is still not known whether or not γ is rational. b) Show that if b n = 1 + 1 2 + 1 3 + ··· + 1 n , then ln( n + 1) < b n ln( n ) + 1. c) Estimate how many terms it would take before b n > 10 6 . How long do you think it would it take for a modern computer to perform this many additions? 3) a) Suppose that a n 0 and that lim n →∞ a n = L . Show that lim n →∞ a n = L . (Hint: Do the cases L = 0 and L > 0 separately. When L > 0 show that a n - L = a n - L a n + L . b)

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.

{[ snackBarMessage ]}

### Page1 / 3

M147A2 - MATH 147 Assignment#2 Due Friday October 9 1 For...

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

View Full Document
Ask a homework question - tutors are online