Lemma 7.1 Convergent/Divergent sums

Lemma 7.2 Comparison test for series

Corollary 7.3 Root Test

Corollary 7.4 Ratio Test

Theorem 7.5 Convergent/Divergent series

Theorem 7.6 Convergent/Divergent power series

Proposition 7.7 Cauchy product formula

Corollary 7.8 Application of the Cauchy product formula

Theorem 7.9 Convergent power series

Corollary 7.10 Power series continuous within disks of convergence

Corollary 7.11 Complex derivatives

Lemma 7.12 More convergent power series

Theorem 7.13 Derivative of e^{x}

Corollary 7.14 Derivative of log(x)

Corollary 7.15 Derivative of a^{x}

Corollary 7.16 Derivative of x^{r}

Lemma 7.17 sin(z) has a positive real root

Theorem 7.18 pi is the smallest positive real root of sin(x)

Lemma 7.19 Closed additive subgroups of **R**

Proposition 7.20 The map of e^{ix} is a bijection

Corollary 7.21 Every non-zero complex number can be expressed in the form re^{(i\theta)}

Proposition 7.22 Taylor Series

Corollary 7.23 Equality of sums

Proposition 7.24 Definition of x^{a}

Theorem 7.25 Definition of f^{k}

Corollary 7.26 Bounds of derivatives

Proposition 7.27 log(x) is equal to its Taylor Series

Proposition 7.28 The number

Proposition 7.29 The number pi is between 2.6 and 3.4

Proposition 7.30 Rearrangements of conditionally convergent series

Proposition 7.31 Rearrangements of absolutely convergent series

Proposition 7.32 Convergence of double series