Gheorgheserban2018ask
a fost răspuns


13 Calculaţi sumele:
b. S = 1 supra 1 + 2 + 1 supra 1 +2 +3 + 1 supra 1 +2 +3 +4 +.....+ 1 supra 1+ 2+ 3+ 4+....+ 2009​

Răspuns :

1/3+1/6+1/10+1/15+...+2/2009*2010=
2/2*3+2/3*4+2/4*5+2/5*6+ ...+2/2009*2010=
2( 1/2*3+1/3*4+1/4*5+...+1/2009*2010)=
1(1/2-1/3+1/3-1/4+1/4-1/5+....+1/2009-1/2010)=
2(1/2-1/2010)=
2(1005-1)/2010=
1004/1005