Question

[Chu Gia Hân]

1/6 + 1/30 + 1/70 + 1/126 + ... + 1/966

Answer 1

[Đức]

3A=2.33​+6.33​+12.31​+20.33​+30.33​+42.33​

3A=\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+\frac{1}{5.6}+\frac{1}{6.7}

3A=\frac{2-1}{1.2}+\frac{3-2}{2.3}+\frac{4-3}{3.4}+...+\frac{7-6}{6.7}

3A=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{6}-\frac{1}{7}

3A=1-\frac{1}{7}=\frac{6}{7}\Rightarrow A=\frac{2}{7}