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tarheelborn
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Homework Statement
Suppose that {a_n} is a divergent sequence of real numbers and c \in R, c <> 0. Prove that {c*a_n} diverges.
Homework Equations
The Attempt at a Solution
I have attempted to solve the problem as a proof by contradiction, but am afraid I am leaving something out. Please confirm my proof is complete or prompt me to add. Thanks!Proof is by contradiction. Suppose {c*a_n} is convergent. This means that |c*a_n - L| < e, for e > 0. Then there is N \in N such that |a_n - L/c| < e/|c|, n >= N. But this is the definition of limit of a sequence, so a_n converges. But this contradicts our problem statement so, in fact, a_n diverges. End of proof.