Question

imi puteti arata va rog cum se face 2 pas cu pas?

Answer 1

Răspuns:

$\frac{2x}{1*3} +\frac{2x}{3*5} +\frac{2x}{5*7} +...+\frac{2x}{19*21} =2\frac{6}{7}$

2x($\frac{1}{1*3} +\frac{1}{3*5} +\frac{1}{5*7}+....+\frac{1}{19*21}) =\frac{20}{7}$

$\frac{1}{1*3} =\frac{1}{2} (\frac{1}{1} -\frac{1}{3} )$

$\frac{1}{3*5} =\frac{1}{2} (\frac{1}{3} -\frac{1}{5} )$

$\frac{1}{5*7} =\frac{1}{2} (\frac{1}{5} -\frac{1}{7} )$

................................

$\frac{1}{19*21} =\frac{1}{2} (\frac{1}{19} -\frac{1}{21} )$

Se   aduna   termen cu termen

$\frac{1}{1*3} +....+\frac{1}{19*21} =\frac{1}{2} (\frac{1}{1} -\frac{1}{3} +\frac{1}{3} -\frac{1}{5}+\frac{1}{5} -\frac{1}{7} +...+\frac{1}{19} -\frac{1}{21} )$=

$\frac{1}{2} (1-\frac{1}{21} )=$

$\frac{1}{2} *\frac{20}{21}$

Expresia  devine

*$2x*\frac{1}{2} *\frac{20}{21} =\frac{20}{7}$

$\frac{x}{21} =\frac{1}{7}$

x$=\frac{21}{7} =3$

Explicație pas cu pas: