Question

Calculati x ori y, unde x=1/2 x 3/4 x 5/6 x 7/8 x...x 99/100, iar y=2/3 x 4/5 x 6/7 x 8/9 x...x 100/101.

Aprecieri oricui îmi răspunde!! ​

Answer 1

$x=\frac{1}{2} \frac{3}{4} \frac{5}{6} \frac{7}{8}...\frac{99}{100} \\\\y=\frac{2}{3} \frac{4}{5} \frac{6}{7} \frac{8}{9}...\frac{100}{101} \\\\x*y=(\frac{1}{2} \frac{3}{4} \frac{5}{6} \frac{7}{8}...\frac{99}{100} )(\frac{2}{3} \frac{4}{5} \frac{6}{7} \frac{8}{9}...\frac{100}{101})$

Se intercaleaza termenii

$x*y=\frac{1}{2}\frac{2}{3}\frac{3}{4}\frac{4}{5}...\frac{98}{99}\frac{99}{100}\frac{100}{101}$

Se se simplifica 2cu2,3cu3,4cu4,...,100cu100

Ramane:

$x*y=\frac{1}{101}$

Answer 2

Răspuns:

Explicație pas cu pas:

ai răspunsul în imagine