Question

Am nevoie urgent de aceasta problema.

Answer 1

Răspuns:

Explicație pas cu pas:

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

1/(k(k+1)/2) = 2/(k(k+1))

1/(1+2) = 1/(2*3/2) = 2/2*3

1/(1+2+3) = 1/(3*4/2) = 2/3*4

..........

1/(1+2+3+...+2015) = 2/2015*2016

S = 2/1*2 + 2/2*3 +2/3*4 + 2/4*5 +...+2/2015*2016 =

2(1-1/2 + 1/2-1/3 + 1/3-1/4 + 1/-1/5 +... +1/2015-1/2016=

2(1 -1/2016) = 2*2015/2016 = 2015/1008