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### Questions (12)

 14 How to solve this equation:$\sqrt{x-\sqrt{x-\sqrt{x-\sqrt{x-5}}}}=5$ 13 prove $\frac{1}{ n+1}+\frac{1}{ n+2}+\cdots+\frac{1}{2n}<\frac{25}{36}$ by mathematical induction 13 prove $\frac{1}{13}<\frac{1}{2}\cdot \frac{3}{4}\cdot \frac{5}{6}\cdot \cdots \cdot \frac{99}{100}<\frac{1}{12}$ 7 Prove $|\vec{a_1}-\vec{b}|+ \cdots +|\vec{a_n}-\vec{b}| > n$ 7 Calculate $1\times 3\times 5\times \cdots \times 2013$ last three digits.

### Reputation (374)

 +5 Prove $\sqrt[3]{60}>2+\sqrt[3]{7}$ +5 prove $\frac{1}{ n+1}+\frac{1}{ n+2}+\cdots+\frac{1}{2n}<\frac{25}{36}$ by mathematical induction +5 how to prove ${{a}_{0}}+{{a}_{1}}x+{{a}_{2}}{{x}^{2}}+\cdots +{{a}_{n}}{{x}^{n}}=0$ has at least one real root in $(0,1)$. +5 Calculate $1\times 3\times 5\times \cdots \times 2013$ last three digits.

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### Tags (6)

 0 inequality × 8 0 elementary-number-theory 0 functions × 2 0 harmonic-numbers 0 induction × 2 0 rational-numbers

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 Mathematics 374 rep 29