Question

URGENT!!! VĂ r=ROG SĂ MĂ AJUTAȚI!
Calculați sumele:
a) $\frac{1}{1+ \sqrt{2} }+ \frac{1}{ \sqrt{2} + \sqrt{3} }+...+ \frac{1}{ \sqrt{8+ \sqrt{9} }} ;$
b) $\frac{1- \sqrt{3} }{ \sqrt{3}}+ \frac{ \sqrt{3}- \sqrt{5} }{ \sqrt{15}}+ \frac{ \sqrt{5}- \sqrt{7} }{ \sqrt{35}}+ \frac{ \sqrt{7}- \sqrt{9} }{ \sqrt{63}}$

Answer 1

1/(1+√2)+1/(√2+√3)+....+1/(√8+√9)=
=(1-√2)/(1-2)+(√2-√3)/(2-3)+....+(√8-√9)/(8-9)=
=-1+√2-√2+√3+.....-√8+√9 = -1+√9

(1-√3)/√3 +(√3-√5)/√15 +(√5-√7)/√35 +(√7-√9)/√63=
=1/√3-1 +1/√5-1/√3 +1/√7-1/√5 +1/√9-1/√7=
=-1  +1/√9=
=-1  +1/3=
=(-3+1)/3=-2/3