Question

Aratati ca a apartine [0,(3);0,5] unde a=1/23+1/34+1/4x5+........+1/29x30

Answer 1

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Answer 2

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] .