1. B


    Prove that, for x, y, z positive, \frac{3+x^4+y^3+z^2}{1+2x^3+3y^2+6z}+\frac{3+y^4+z^3+x^2}{1+2y^3+3z^2+6x}+\frac{3+z^4+x^3+y^2}{1+2z^3+3x^2+6y}>=\frac{3}{2}
  2. O

    inequality 2

    Prove the following inequality ,where a,b,c are positive Nos: \frac{1}{b(a+b)}+\frac{1}{c(b+c)}+\frac{1}{a(c+a)}\geq\frac{27}{2(a+b+c)^2}
  3. O


    prove that: (a+b+c)\geq\frac{(\sqrt a+\sqrt b+\sqrt c)^2}{3} I tried by expanding the square
  4. tahirimanov19


    $$\left| \sin \left( \sum_{k=1}^n x_k \right) \right| \le \sum_{k=1}^n \sin (x_k)$$ $\; \; \; \; \; (0 \le x_k \le \pi ; \; \; k=1,2,...,n)$
  5. E

    Solve the inequality 2/x > 3x

    pls help:)
  6. idontknow

    Cannot prove inequality

    Prove that \: a_n =\frac{|\sin(n)|}{n} +\frac{|\sin(n+1)|}{n+1}>\frac{1}{6}\; ,n\in \mathbb{N}.
  7. idontknow

    Inequality #2 without calculus

    Given x^y < y^x , where x>y \geq \lambda >0, find the range of \lambda . Without calculus!
  8. idontknow

    Prove inequality without calculus

    Prove that a^b < b^a , for a>b\geq 3.
  9. A

    Hard inequality

    Given a,b,c>=1 and a+b+c=9. Prove that (√a+√b+√c)^2>=ab+bc+ca.
  10. idontknow

    Prove inequality

    If 0<a_1 < a_2 < a_3 <... <a_n < \frac{\pi}{2} . Prove that \tan(a_1 ) <\frac{sin(a_1) +sin(a_2 ) +sin(a_3)+...+sin(a_n )}{cos(a_1 ) +cos(a_2 )+cos(a_3 )+...+cos(a_n )}<\tan(a_n ) .
  11. D

    Lotka-Volterra with periodic coefficients differential inequality

    I would like to ask which transformation should I use to recive from this Lotka-Volterra inequality x′=x(a−bx−cy)<x(a−bx), this differential form x(t)\leq \frac{x(T)e^{A(t)}}{1+x(T)\int \limits_{T}^{t}e^{A(s)}b(s)ds}, \text{where} A(t)=\int_T^t a(s)ds.
  12. B

    Probability inequality problem

    Suppose A and B are independent and identically distributed. For the purposes of this problem, x and y are not capped at 1, but are definitely at least 0. Pr(A)<x Pr(B)<y Pr(AUB)<? I know Pr(AUB)<x+y, but is it possible to make the right side any lower? What is the lowest it can be given the...
  13. idontknow

    Integral inequality

    Compare e with : \int_{0}^{-\infty } e^{e^x } \cdot e^x dx .
  14. B

    Proof for a challenging inequality

    I have something I believe to be true, but I'm uncertain, so I'm looking for a proof. For positive real numbers a,b,c,d Prove that if a>=b and c<=d, then a/c <= b/d
  15. idontknow

    Inequality similiar to harmonic sum

    For which values of n the inequality holds true : 1+\frac{1}{2}+\frac{1}{3}+...+\frac{1}{n^4 }=\sum_{j=1}^{n^4 }j^{-1} >2n.
  16. idontknow

    Prove inequality

    Prove: e^{n^2} \left(1^1 \cdot 2^2 \cdot 3^3 \cdot ...\cdot n^n \right)\leq n^{n^2 + n + 6}.
  17. idontknow

    Inequality with sqrt

    Prove that \sqrt{1} +\sqrt{2} +...+\sqrt{n} \geq n.
  18. idontknow

    Solve inequality

    For which values of N : \; \sum_{j=1}^{N} j^{-1} >\frac{N}{\ln(N+1)}.
  19. idontknow

    Prove inequality without calculator

    Prove inequality: \sqrt{2} +\sqrt{3} >\pi .
  20. A

    Help : Deriving an inequality related to Lucas Sequence

    Hi, I am studying a paper by Yann Bugeaud (click here), on page 13 there is an inequality (16) as given below- $\Lambda:=\left|\left(\frac{\alpha(\gamma-\delta)}{\gamma(\alpha-\beta)}\right)\left(\frac{\gamma^{s}}{\alpha^{r}}\right)^{-d}-1\right| \ll \alpha^{-\eta r d}$ which is obtained from...