Question

Найдите сумму: 1/(1+v2)+1/(v2+v3)+...+1/(vn+vn+1), если n=99.

Answer 1

1/(√1+√2)+1/(√2+√3)+......+1/(√98+√99)+1/(√99+√100)=
=(√1-√2)/(1-2)+(√2-√3)/(2-3)+......+(√98-√99)/(98-99)+(√99-√100)/(99-100) =
=(-√1+√2)+(-√2+√3)+......+(-√98+√99)+(-√99+√100)=
=√100-√1=10-1=9