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 8 Prove that: $\frac{a}{a+1}+\frac{b}{(a+b+1)^2}+\frac{1}{a+b+1}\le1$ 5 Find the constant K in probability distribution? 5 What is the formula for this exponentially growing “stairs”? 5 Probability that the last ball is white? 4 How do you distinguish the difference between a negative sign and a minus sign in Algebra

### Reputation (1,251)

 +5 Material derivative of a material vector field +5 Evaluate integral $\int_0^\frac{\pi}{2} \ln\left(\frac{1+a\cos x}{1-a\cos x}\right) \frac{\mathrm{d} x}{\cos x}$ for $\left|a\right|<1$ +10 Odds of 1 out of 7 NFL teams making the playoffs +10 Proof that this set is convex

### Questions (10)

 22 Math contest: Find number of roots of $F(x)=\frac{n}{2}$ involving a strange integral. 7 Evaluate integral $\int_0^\frac{\pi}{2} \ln\left(\frac{1+a\cos x}{1-a\cos x}\right) \frac{\mathrm{d} x}{\cos x}$ for $\left|a\right|<1$ 5 Coordinate method for solving first order linear PDE 5 Test the convergence of: $1+\frac{1}{2}-\frac{1}{3}+\frac{1}{4}+\frac{1}{5}-\frac{1}{6}+\cdots$ 2 Identify infinite sum: $\sum\limits_{n=0}^{+\infty}\frac{x^{4n}}{(4n)!}$

### Tags (40)

 17 probability × 7 5 linear-algebra × 2 8 contest-math × 4 5 graphing-functions 8 inequality 4 multivariable-calculus × 2 6 algebra-precalculus × 2 4 arithmetic 5 functions × 2 3 power-series × 4

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