Demostrar que $1-\frac{1}{2}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{199}-\frac{1}{200}=\frac{1}{101}+\frac{1}{102}+...+\frac{1}{200}.$

Question

Yo quiero probar esta escuela secundaria problema de álgebra. demostrar que $$1-\frac{1}{2}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{199}-\frac{1}{200}=\frac{1}{101}+\frac{1}{102}+...+\frac{1}{200}.$$ Por favor me ayude. Gracias.

Answer 1

$1 - \frac{1}{2} + \frac{1}{3} - \frac{1}{4} + ... + \frac{1}{199} - \frac{1}{200}$

$= (1 + \frac{1}{2} + \frac{1}{3} + \frac{1}{4} + ... + \frac{1}{199} + \frac{1}{200}) - 2 * (\frac{1}{2} + \frac{1}{4} + ... + \frac{1}{200})$

$= (1 + \frac{1}{2} + \frac{1}{3} + \frac{1}{4} + ... + \frac{1}{199} + \frac{1}{200}) - (\frac{1}{1} + \frac{1}{2} + ... + \frac{1}{100})$

$= \frac{1}{101} + \frac{1}{102} + ... + \frac{1}{200}$