# cwk709394

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# 18 Questions

 17 Prove a $\pi$ inequality: $\left(1+\frac1\pi\right)^{\pi+1}<\pi$ 6 prove by induction : $\frac{(1-a^n)}{1-a}+\frac{(1-a^n)(1-a^{n-1})}{1-a^2}+…+\frac{(1-a^n)(1-a^{n-1})…(1-a)}{1-a^n}=n$ 4 Prove or disprove the system about $n$th power has only one solution $x=y=1$ 4 Does $\lim_{n\to\infty}\underset{n}{\underbrace{\cos(\cos(…\cos x))}}$ exist? [duplicate] 3 solve the differential equation : $(x^2+xy)\frac{dy}{dx}-(3xy+y^2)=0$

# 296 Reputation

 +5 Evalulate $\int_{-\infty}^{\infty}\frac{1}{(1+x^{2n})^2}dx$ by using residue theorem +10 Prove $\sum_{i=0}^{n}\left(x_{i}^{n}\prod_{0\leq k\leq n}^{k\neq i}\frac{x-x_k}{x_i-x_k}\right)=x^n$ +5 integration inequality +5 Prove or disprove the system about $n$th power has only one solution $x=y=1$

 0 Combinatorial proof of an identity

# 29 Tags

 0 calculus × 5 0 limits × 2 0 integration × 5 0 trigonometry × 2 0 definite-integrals × 4 0 induction × 2 0 differential-equations × 2 0 inequality × 2 0 derivatives × 2 0 pde

# 1 Account

 Mathematics 296 rep 29