Question

Calculati:

$\frac{1}{\sqrt{5}+\sqrt{3} } +\frac{1}{\sqrt{7}+\sqrt{5} } +...+\frac{1}{\sqrt{99} +\sqrt{97} }$

Answer 1

Răspuns:

1/(√5+√3)=(√5-√3)/(√5+√3)(√5-√3)=(√5-√3)/(5-3)=(√5-√3)/2

1/(√7+√5)=(√7-√5)/(√7+√5)(√7-√5)=(√7-√5)/2

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

1/(√99+√97)=(√99-√97)/(√99+√97)(√99-√97)=(√99-√97)/2

1/(√5+√3)+1/(√7-√5)+...+1/(√99+√97)=1/2[√5-√3+√7-√5+....+√99-√97]=√99

Explicație pas cu pas: