Question

1/1*2 + 1/2*3 + 1/3*4 +...+ 1/27*28=?

Answer 1

$\frac{1}{1 \times 2} + \frac{1}{2 \times 3} + ... + \frac{1}{27 \times 28} \\ \\ = \frac{2 - 1}{1 \times 2} + \frac{3 - 2}{2 \times 3} + ... + \frac{28 - 27}{27 \times 28} \\ \\ = \frac{2}{1 \times 2} - \frac{1}{1 \times 2} + \frac{3}{2 \times 3} - \frac{2}{2 \times 3} + ... + \frac{28}{27 \times 28} - \frac{27}{27 \times 28} \\ \\ = \frac{1}{1} - \frac{1}{2} + \frac{1}{2} - \frac{1}{3} + \frac{1}{3} - ... + \frac{1}{27} \\ \\ = \frac{1}{1} - \frac{1}{27} \\ \\ = \frac{26}{27}$