Question

Aratati ca S=1/√2+1 +1/√3+√2 +1/√4+√3 =2.

Answer 1

S=1/(√2+1) +1/(√3+√2) +1/(√4+√3) =
=(√2-1)/(√2+1)(√2-1) +(√3-√2) /(√3+√2)(√3-√2) +(2-√3)/(2+√3)(2-√3) =
=(√2-1)/(2-1) +(√3-√2) /(3-2) +(2-√3)/(4-3) =
=√2-1 +√3-√2 +2-√3 =
=-1 +2 =1

Answer 2

S=1/(radical2+1) +1/(radical3+radical2) +1/(radical4+radical3) 
=(rad2-1)/(rad2+1)(rad2-1) +(rad3-rad2) /(rad3+rad2)(rad3-rad2) +(2-rad3)/(2+rad3)(2-rad3) 
=(rad2-1)/(2-1) +(rad3-rad2) /(3-2) +(2-rad3)/(4-3) 
=rad2-1 +rad3-rad2 +2-rad3 
= -1 +2 
=    1