Question

Calculati suma:1/1+ radical din 2 +1/radical din 2 + radical din 3+...+1/radical din 8+radical din 9

Answer 1

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

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