Question

Calculați :

S=1:(1×5)+1:(5×9)+1:(9×13)+...+1:(81×85)

Answer 1

[tex]S= \frac{1}{4} ( \frac{5-1}{1\cdot5} + \frac{9-5}{5\cdot9}+ ...+\frac{85-81}{81\cdot85})\\ S=\frac{1}{4} ( 1- \frac{1}{5} + \frac{1}{9} +...+\frac{1}{81} + \frac{1}{85} )\\ S=\frac{1}{4} ( 1-\frac{1}{85} )\\ S=\frac{1}{4} \cdot\frac{84}{85} \\ S= \frac{21}{85} [/tex]