Răspuns:
[tex]\frac{2x}{1*3} +\frac{2x}{3*5} +\frac{2x}{5*7} +...+\frac{2x}{19*21} =2\frac{6}{7}[/tex]
2x([tex]\frac{1}{1*3} +\frac{1}{3*5} +\frac{1}{5*7}+....+\frac{1}{19*21}) =\frac{20}{7}[/tex]
[tex]\frac{1}{1*3} =\frac{1}{2} (\frac{1}{1} -\frac{1}{3} )[/tex]
[tex]\frac{1}{3*5} =\frac{1}{2} (\frac{1}{3} -\frac{1}{5} )[/tex]
[tex]\frac{1}{5*7} =\frac{1}{2} (\frac{1}{5} -\frac{1}{7} )[/tex]
................................
[tex]\frac{1}{19*21} =\frac{1}{2} (\frac{1}{19} -\frac{1}{21} )[/tex]
Se aduna termen cu termen
[tex]\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} )[/tex]=
[tex]\frac{1}{2} (1-\frac{1}{21} )=[/tex]
[tex]\frac{1}{2} *\frac{20}{21}[/tex]
Expresia devine
*[tex]2x*\frac{1}{2} *\frac{20}{21} =\frac{20}{7}[/tex]
[tex]\frac{x}{21} =\frac{1}{7}[/tex]
x[tex]=\frac{21}{7} =3[/tex]
Explicație pas cu pas:
