Question

1/1+(1/1+2)+(1/1+2+3)+...+(1/1+2+.. +100)=

Answer 1

Se aplica gauss in fiecare si rezulta =1/1+2/2*3+2/3*4+....+2/100*101=1+2(1/2*3+1/3*4+....+1/100*101) Dar noi stim ca 1/100*101 =1/100-1/101 Asadar rezulta 1+2(1/2-1/3+1/3-1/4+....+1/100-1/101)= se reduc dat scaderii si rezulta 1+2(1/2-1/101)=1+1-2/101=2-2/101=(202-2)/101=200/101=1.98