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Mathematics
余志祥's user avatar
余志祥's user avatar
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余志祥
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5
Let $\left<a_i\right>,\left<b_i\right>$ be real sequences satisfied as following conditions：
Mar 24, 2022
3
Evaluate $\frac{q}{1+q^2}+\frac{q^2}{1+q^4}+\frac{q^3}{1+q^6}$, where $q^7=1$ and $q\neq 1$.
Apr 29, 2020
3
$ax^3+bx^2+cx+d=0$ with coefficient $a>b>c>d>0$. Show that the magnitude of all its roots is less than $1$.
Jul 27, 2023
3
Is the function $f(x)=\int_0^\pi \ln |x+\cos(t)| dt$ differentible in interval (-1, 1)？
Mar 29
3
$ax^3+bx^2+cx+d=0$ with coefficient $a>b>c>d>0$. Show that the magnitude of all its roots is less than $1$.
Jul 27, 2023
2
Is the series $\sum^\infty_{n=1}\left( a^{\frac{1}{n}}+a^{-\frac{1}{n}}-2 \right)$ converging?
Jan 21, 2020
2
$A+B+C+D=\pi$, and $0\leq A,B,C,D \leq \frac{\pi}{2}$. Prove that $\sin^4(A)+\sin^4(B)+\sin^4(C)+\sin^4(D)\leq 2$
Feb 6, 2022
2
Evaluate $\lim_{n\ \rightarrow\ \infty\ }\ \left(\frac{\sqrt{1\times3}+\sqrt{2\times4}+\cdots\sqrt{n\times\left(n+2\right)}}{n}-\frac{n}{2}\right)$
Apr 13, 2023
1
Show that $f(x)=\sqrt{\sin x}$ is continuous in the interval $[0,\pi]$.
Apr 23, 2020
1
Sequence $\left\{ a_n\right\}$ defined by $a_1=4$ , and $a_{n+1}=\sqrt{a_n+6}$. Prove that $\left| a_{n+1}-3\right|<\frac{1}{3}\left|a_n-3\right|$.
May 7, 2020