Intereting Posts

Zeros of the decimal representation of $k!$
Questions on symmetric matrices
How to prove that $\cos\theta$ is even without using unit circle?
Representing every positive rational number in the form of $(a^n+b^n)/(c^n+d^n)$
$QR$ decomposition of rectangular block matrix
Prove that $\sigma(AB) \backslash \{0\} = \sigma(BA)\backslash \{0\} $
|f| is periodic implies f is periodic
Exercise 31 from chapter 4 (“Hilbert Spaces: An Introduction”) of Stein & Shakarchi's “Real Analysis”
Integral involving Clausen function ${\large\int}_0^{2\pi}\operatorname{Cl}_2(x)^2\,x^p\,dx$
Generating series using partitions
How to compute $\sum^n_{k=0}(-1)^k\binom{n}{k}k^n$
“Visual” interpretation of the Bott Periodicity for complex vector bundles
Continuous function $f:E\rightarrow F$ with closed graph in $E\times F$ implies $F$ compact
definite integral without using complex line integral
Lagrange inversion theorem application

Question is to check if : $\sum_{n=1}^{\infty}\frac{(\log\log2)^n}{n!}>\frac{3}{5}$

the problem is that i am sure that this series$\sum_{n=1}^{\infty}\frac{(\log\log2)^n}{n!}$ is convergent (if it is not then i would be very happy as i will then be done.)

I would be thankful if someone can help me out with solving this.

- How to calculate $2^{\sqrt{2}}$ by hand efficiently?
- (ZF)subsequence convergent to a limit point of a sequence
- Harmonic Function with linear growth
- Computability, Continuity and Constructivism
- Closed form of $\int_{0}^{\infty} \frac{\tanh(x)\,\tanh(2x)}{x^2}\;dx$
- Is every compact subset of $\Bbb{R}$ the support of some Borel measure?

- If $f(xy)=f(x)f(y)$, then $f(x)=x^b$.
- A sub-additivity inequality
- Putnam and Beyond AM-GM help
- Series expansion of infinite series raised to the $n$th power
- Problem similar to folland chapter 2 problem 51.
- A strange “pattern” in the continued fraction convergents of pi?
- Show that $C_1= [\frac{k}{2^n},\frac{k+1}{2^n})$ generates the Borel σ-algebra on R.
- Non-increasing sequence of positive real numbers with prime index
- Question about arithmetic–geometric mean
- Prove continuity for cubic root using epsilon-delta

Hint : Think about the Taylor expansion of Exp[x]; this could help you answering both questions.

- ODE introduction textbook
- To show that $\sqrt{z^2-1}=\exp(\frac{1}{2} \log(z^2-1))$ is analytic in the plane minus
- What does this theorem in linear algebra actually mean?
- Heat flow in 1D bar: why are the eigenfunctions used in the Fourier series orthogonal?
- How to prove that this series is a metric: $d(x,y):=\sum_{i=0}^\infty \frac{|x_i -y_i|}{2^i (1+|x_i-y_i|)}$
- Induction, 0'1 and 1's sequence fun question
- How many $6$-lentgh increasing sequence are there from $1$ to $49$?
- Radius of Convergence of $\sum ( \sin n) x^n$.
- Curvature of given metric space
- Trouble to prove L'Hopital theorem to the case $\infty/\infty$
- Conditional expectation of $\max(X,Y)$ and $\min(X,Y)$ when $X,Y$ are iid and exponentially distributed
- Trigonometric identities using $\sin x$ and $\cos x$ definition as infinite series
- Approximation of conditional expectation
- How to compute $\lim _{x\to 0}\frac{x\bigl(\sqrt{3e^x+e^{3x^2}}-2\bigr)}{4-(\cos x+1)^2}$?
- What is $L^p$-convergence useful for?