Aplicam formula de calcul 1 /k·(n+k)=1/n ·(1/k -1 /n+k) unde n,k∈N\{0} .
Asadar a=1 /2·3 +1 /3·4 +1 /4·5 +...+1 /29·30 =1/2 -1/3 +1/3 -1/4 +1/4 -1/5 +...+1/29 -1/30 <=>
a=1/2 -1/30 <=> a=14/30 <=> a=7/15 ;
0,(3) <= 7/15 => 3/9 <= 7/15 <=> 1/3 <= 7/15 => 15 <= 21 ,care este adevarat si 7/15 <= 0,5 => 7/15 <= 1/2 => 14 <= 15 ,care este adevarat => a∈[0,(3),0,5] .
