Question

Calculati:  $\frac{1}{2} + \frac{1}{6}+ \frac{1}{12}+ \frac{1}{20}+.....+ \frac{1}{90}$

Answer 1

$\frac{1}{2}+ \frac{1}{6}+ \frac{1}{12}+ \frac{1}{20}+ \frac{1}{30}+ \frac{1}{42}+ \frac{1}{56}+ \frac{1}{72}+ \frac{1}{90}$

2   = 2  
6   = 2 * 3
12  = 2² * 3
20  = 2² * 5
30  = 2 * 3 * 5
42  = 2 * 3 * 7
56  = 2³ * 7
72  = 2³ * 3²  
90  = 2 * 3² * 5
cmmmc = 2³ * 3² * 5 * 7 = 2520

$\frac{1260+420+210+126+84+60+45+35+28}{2520}= \frac{2268}{2520}= \frac{9}{10}$