MATH220 April 2005
• Q1 • Q2 • Q3 (a) • Q3 (b) • Q3 (c) • Q4 • Q5 • Q6 • Q7 • Q8 • Q9 • Q10 • Q11 •
is a bounded function and that is a sequence that converges to 0. Prove that
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Show that if is a sequence converging to zero and M is a constant then the sequence also converges to zero.
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Since is bounded there exists a constant M such that
We will show that converges to zero. Let . Since converges to zero there exists a positive integer Nε such that
This shows that converges to zero.
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