Question

Calculati valoarea sumei:
S=1+(1-1/2)+(1-1/3)+(1-1/4)+........+(1-1/2011)-(1/2+2/3+3/4+........+2010/2011)=?

Answer 1

1-1/2=1/2; 1-1/3=2/3; 1-1/4=3/4.........1-1/2011=2010/2011 deci
S=1+(1/2+2/3+3/4+....210/2011)-(1/2+2/3+3/4+....210/2011) rezulta S=1