Math topic中文

Telescoping and splitting fractions

Split each fraction into a difference of two terms so that intermediate terms cancel, e.g. 1/(n(n+1)) = 1/n - 1/(n+1).

Learn these first

Four operations on decimals and fractions

Practice questions

1等差数列 $\{a_{n}\}$ 的前 $n$ 项和为 $S_{n}$ ，数列 $\{b_{n}\}$ 为等比数列， $S_{n}\text{=}n^{2}\text{+}n$ ， $b_{1}\text{=}a_{1}\text{,}b_{2}\text{=}\dfrac{a_{1}a_{2}}{2}\text{.}$ …
2已知在数列 $\{a_{n}\}$ 中， $a_{1}=1$ ，其前 $n$ 项和为 $s_{n}$ ，且 $a_{n}= \dfrac {2 s_{ n }^{ 2 }}{2s_{n}-1}(n\geqslant 2)(1)$ 证明 $\{ \dfrac {1}{s_{n}}\}$ …
3What is the value of the product $(1 + \frac{1}{1}) \cdot (1 + \frac{1}{2}) \cdot (1 + \frac{1}{3}) \cdot (1 + \frac{1}{4}) \cdot (1 + \frac{1}{5}) \cdot (1 + \frac{1}{6})$ …
4已知数列 $\{a_{n}\}$ 满足 $a_{1}=1$ ，且 $a_{n+1}=\dfrac{2{{a}_{n}}}{3{{a}_{n}}+2}(n\in N^{*}).(1)$ 证明：数列 $\left\{\dfrac{2}{{{a}_{n}}}\right\}$ …