Question

Calculati:
S1=1/2+1/6+1/12+1/20+....1/90
S2=1/30+1/42+1/56+1/72+....1/2652

Answer 1

S1 = 1/1·2 + 1/2·3 + 1/3·4 +........+1/9·10 = (1/1 - 1/2) + (1/2 - 1/3) + (1/3 -1/4) + ......+ (1/9 - 1/10) = 1/1 - 1/10 = 9/10
S2 = 1/5·6 + 1/6·7 + 1/7·8 +....+ 1/51·52 = (1/5-1/6) + (1/6-1/7) + (1/7-1/8) + ... .....+(1/51 - 1/52) = 1/1 - 1/52 = 51/52