Question

Calculati:
S=$\frac{1}{1x2}$+$\frac{1}{2x3}$+$\frac{1}{3x4}$+...+$\frac{1}{9x10}$

Answer 1

S=(1-1/2)+(1/2-1/3)=...+(1/9-1/10=1-1/2+1/2-1/3+1/3-1/4+...+1/9-1/10=1-1/10=9/10