Răspuns:
[tex](\frac{1}{1*2}+\frac{1}{2*3}+\frac{1}{3*4}+...+\frac{1}{44*45}) =(\frac{1}{1}-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{44} -\frac{1}{45} )=(\frac{1}{1} -\frac{1}{45})=\frac{44}{45}.\\(\frac{1}{45*46}+\frac{1}{46*47}+\frac{1}{47*48}+...+\frac{1}{89*90}) =(\frac{1}{45}-\frac{1}{46}+\frac{1}{46}-\frac{1}{47}+\frac{1}{47}-\frac{1}{48}+...+\frac{1}{89} -\frac{1}{90} )=(\frac{1}{45} -\frac{1}{90} )=(\frac{2}{90} -\frac{1}{90} )=\frac{1}{90} \\[/tex]
[tex]Deci~x=\sqrt{29*30*[\frac{44}{45}-\frac{1}{90} ]}=\sqrt{29*30*[\frac{88}{90}-\frac{1}{90} ]}=\sqrt{29*30*\frac{87}{90} }=\sqrt{29^{2}}=29.[/tex]
Explicație pas cu pas:
