Question

Calculati suma: 201/2+601/6+1201/12+...+9001/9. Dau coroana

Answer 1

S = (100 + 1/2) + (100+1/6) + (100 + 1/12) +..............+(100 + 1/90) =
= 100· 9+ 1/1 ·1/2 + 1/2·1/3 + 1/3·1/4 .......................1/9 ·1/10=
= 900 + 1/1 - 1/2 + 1/2 - 1/3 + 1/3- 1/4 +....................1/9 - 1/10 =
= 900 + 1/1 - 1/10 = 900 + 9/10 = 9009/10 = 900,9

Answer 2

S=(200+1)/2+(600+1)/6+(1200+1)/12+......+(9000+1)/90
S=100+1/2+100+1/6+100+1/12+......+100+1/90
S=900+1/2+1/6+1/12+.......+1/90
..................
S=900+1/2+1/3+1/15
S=900+15/30+10/30+2/30
S=900+(15+10+2)/30
S=900+27/30
S=900+9/10
S=900,9