Răspuns:
x = 1
Explicație pas cu pas:
x ∈ N*
1/(1·2) +1/(2·3) + ......+1/[x(x+1)] < 5/6 <=>
1/1 - 1/2 + 1/2 - 1/3 + 1/3 -1/4 +1/4 - 1/5 +..... +1/x - 1/[x(x+1)] < 5/6 <=>
1 - 1/[x(x+1)] < 5/6 <=> 1-5/6 < 1/[x(x+1)] <=>
1/6 < 1/[x(x+1)] <=> x(x+1) < 6
x(x+1) = produsul a doua numere consecutive => x < 2 ; x≠0 =>
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Răspuns:
x = 1
Explicație pas cu pas:
x ∈ N*
1/(1·2) +1/(2·3) + ......+1/[x(x+1)] < 5/6 <=>
1/1 - 1/2 + 1/2 - 1/3 + 1/3 -1/4 +1/4 - 1/5 +..... +1/x - 1/[x(x+1)] < 5/6 <=>
1 - 1/[x(x+1)] < 5/6 <=> 1-5/6 < 1/[x(x+1)] <=>
1/6 < 1/[x(x+1)] <=> x(x+1) < 6
x(x+1) = produsul a doua numere consecutive => x < 2 ; x≠0 =>
x = 1