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### Questions (13)

 6 Prove that (M,+,*) is a field 4 Show that $\sum_{k=1}^\infty \frac{1}{k!}$ converges without the Ratio Test 3 Properties of solutions of the functional equation $f(kx) = kf(x)$ 2 Do there exist sequences with these properties and these limit points? 2 Proof that the sequence is divergent

### Reputation (138)

 +5 Properties of solutions of the functional equation $f(kx) = kf(x)$ +10 Prove that (M,+,*) is a field +5 Convergence of a serie depending on an exponent +5 Show that $\sum_{k=1}^\infty \frac{1}{k!}$ converges without the Ratio Test

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 1 vector-analysis 0 analysis 0 real-analysis × 8 0 axioms 0 sequences-and-series × 7 0 roots 0 convergence × 5 0 functional-equations 0 combinatorics × 2 0 supremum-and-infimum

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