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3h
comment Given $|f'(x)|\leq r<1$ show that $f(x)=x$ is unique solution
I think Lagrange's Mean Value Theorem is useful here.
1d
comment Evaluate $\lim_{n\to1^+}\left({\zeta(n)-\dfrac{1}{n-1}}\right)$
For real number $x>0$ and $s\neq 1$ such that $\Re{(s)}>0$ we have $$\zeta(s)=\sum_{1 \le n \le x} \frac{1}{n^s} + \frac{x^{1-s}}{s-1}+\frac{\{x\}}{x^s}-s\int_x^{\infty}\frac{\{u\}}{u^{s+1}}\,du.‌​$$ From that you can (for $x=1$) find that $$\zeta(s)=\frac{s}{s-1}-s\int_1^{\infty} \frac{\{u\}}{u^{s+1}}\,du,$$ so zeta has pole in $s=1$ and...That might help.
Dec
15
reviewed Approve Why does this nonlinear ODE solution not work?
Dec
14
revised Find the probability density function of $Y = 4X_1 – X_2$
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Dec
13
reviewed Reject Is there any fault in this proof?
Dec
13
reviewed Reject A question about Heine-Borel Theorem.
Dec
13
reviewed Edit A closed ball in $l^{\infty}$ is not compact
Dec
13
revised A closed ball in $l^{\infty}$ is not compact
formatted now...
Dec
13
reviewed Approve Completing a metric space
Dec
13
reviewed Approve solving an equation by fixed point theorem
Dec
13
reviewed Approve How to prove a set is nowhere dense?
Dec
13
reviewed Reject Differential forms, number of zeros on disk
Dec
13
reviewed Reject Let Z ∼ N(0,1). Find the probability density function of |Z|
Dec
13
reviewed Approve Suppose $X \sim \mathrm{Exp}(\lambda)$ and $Y = \ln(X)$. Find the probability density function of $Y$ .
Dec
13
comment convergence of infinite series $\sum_{n=1}^\infty \frac{x^n}{(1+x)(1+x^2)(1+x^3)\cdot\cdot\cdot (1+ x^n)}$
That is true, but, you probably meant $k=n$ in last inequality?
Dec
13
revised Other method show that $ A(x)=x^2+x+1=0$ has a zeros in $\mathbb{R}$ but why this contradiction?
deleted 11 characters in body; edited title
Dec
13
revised How to find $\lim\limits_{z \to z_0} \frac{{\overline z}^2-{\overline z_0}^2}{z-z_0}$
added 25 characters in body; edited title
Dec
8
awarded  Caucus
Nov
21
comment Using Vieta's Formulas to find expression involving polynomial roots
$1/a_1+1/a_2+1/a_3=(a_2 a_3 +a_1 a_3+a_1 a_2)/(a_1 a_2 a_3)$ and en.wikipedia.org/wiki/Vieta%27s_formulas
Nov
11
revised A basis $B$ is orthonormal if and only if $\langle f,g \rangle=[f]_B\cdot [g]_B$ for all $f$ and $g$ in $V$
added 47 characters in body; edited title