Question

Calculati:$\frac{5}{3}$+$\frac{32}{15}$+$\frac{107}{35}$+...+$\frac{31982}{1599}$-$\frac{40}{41}$ Va rog!

Answer 1

A = (3·1 + 2)/3 + (15·2 + 2)/15 + (35·3 +2)35 +........+ (1599·20+2)/1599 - 40/41 
= (1+2 + 3 +.....+20) + (2/3 + 2/15 + 2/35 +.....+ 2/1599) - 40/41
1 + 2+ 3+.....+20 = 20·21/2 = 210 
s = 2/3 + 2/15 + 2/35 +....+ 2/1599 =1/1 - 1/3 + 1/3 -1/5 + 1/5 -1/7 +...+1/39 -1/41 = 1/1 - 1/41 = 40/41
A = 210 + 40/41 - 40/41 = 210