Mean value theorem sum of $\frac{1}{f ' (x _k)}$
113633
sum of series using mean value theorem
90556
Proof of the unbounded-ness of $\sum_{n\geq 1}\frac{1}{n}\sin\frac{x}{n}$
64485
Proving $\displaystyle\lim_{h\to0}\frac{f(x+h)-2f(x)+f(x-h)}{h^2}=f''(x)$
48642
Let $f(n) = \sum_{(k,n)=1} e^\frac{2\pi ik}{n}$. Show that $f(n) = \sum_{k=1}^{n}\left(\sum_{d\mid (k,n)} \mu(d)e^{\frac{2\pi ik}{n}} \right) $
77645
Generalized mean value theorem
11387
Mean Value Theorem: $\frac{2}{\pi}<\frac{\sin x}{x}<1$
34496
Proof that $e=\sum\limits_{k=0}^{+\infty}\frac{1}{k!}$
97720
Asymptotic behavior of $\sum\limits_{k=1}^n \frac{1}{k^{\alpha}}$ for $\alpha > \frac{1}{2}$
3772
About the continuity of the function $f(x) = \sum\limits_k2^{-k}\mathbf 1_{q_k \leq x}$
70621
Question concerning the mean-value property
129801
Finding a closed form for $\sum^{n}_{k=1} \frac{k}{(k+1)!} $
107789
Sum of $\sum \limits_{n=0}^{\infty} \frac{1}{(kn)!}$
94489
Mean value property implies harmonicity
53038
Show that $\frac{P(z)}{Q(z)} = \sum_{k=1}^{n}\frac{P(\alpha_k)}{Q'(\alpha_k)(z-\alpha_k)}$
78599
How to prove that $\frac{b-a}{\sqrt{1-a^2}}<\sin^{-1}b-\sin^{-1}a<\frac{b-a}{\sqrt{1-b^2}}$ by using Mean Value Theorem?
111255
Gauss's mean value theorem problem
135700
Show that $\lim_{n \to \infty} (1/n)\sum_{i=1}^n f(x_i)$ exists