Question

Rezolvați va rog
Sa aparțină de N
Dau coroana​

Answer 1

Răspuns:

Explicație pas cu pas:

$1 + \frac{3}{2} + \frac{5}{4} +\frac{7}{6} +...+\frac{1999}{1998} -(1 + \frac{1}{2} + \frac{1}{4} +\frac{1}{6} +...+\frac{1}{1998} )=$

$= (1 - 1) + (\frac{3}{2} -\frac{1}{2} )+ (\frac{5}{4} -\frac{1}{4} )+ (\frac{7}{6} -\frac{1}{6} )+...+ (\frac{1999}{1998} -\frac{1}{1998} )=$

$= \frac{3-1}{2} + \frac{5-1}{4} + \frac{7-1}{6} +...+ \frac{1999-1}{1998} =$

$= \frac{2}{2} + \frac{4}{4} + \frac{6}{6} +...+ \frac{1998}{1998} =$

$= \frac{2}{2}( \frac{1}{1} + \frac{2}{2} + \frac{3}{3} +...+ \frac{999}{999}) =$

$=1*(1 + 1 + 1 + ... +1) =$ (de 999 ori)

$=199$

199 ∈ N