Proving Modified Taylor expansion of $e^x$ (negative sign for odd powers) is always positive when n is EVEN.
27494
$P_n(x):=1+ \sum_{m=1}^n\dfrac{x^m}{m!}$ has no real root for even $n$ and exactly one real root for odd $n$
100234
Proving that $x^n$ converges to $0$ whenever $|x| < 1$
114506
Expansion of $(1+\sqrt{2})^n$
59481
Even and odd functions for Taylor serie
133496
is $\sqrt{x}$ always positive?
19914
Closed form for $\sum_{n=0}^{\infty} \binom{n+k}{k} x^n$ (Negative Binomial Theorem)
16660
Prove that any positive number has an $n$th root
154288
proof that Even powers of an odd function's taylor polynomial vanish
124277
Taylor Series for $\log(x)$
39270
Showing that $e^x > 1+x$
156312
Taylor expansion for $\arcsin^2{x}$
17504
Divergent infinite series $n!e^n/n^n$ - simpler proof of divergence?
83517
Taylor series of Infinitely differentiable function with nonnegative derivatives
21407
Every power series is the Taylor series of some $C^{\infty}$ function
43476
An exponential equation over positive real numbers $4^x+14^x+3^x=11^x+10^x$
55266
Prove that $(n+1)^{n-1}<n^n$
80164
Taylor expansion of a function containing QPochhammer[q, q, n]