Question

Find the value  of n if

\(\frac{1}{\sqrt{ }1+\sqrt{ }2}+\frac{1}{\sqrt{ }2+\sqrt{ }3}+...+\frac{1}{\sqrt{ }n-1+\sqrt{ }n}\)

Answer 1

\(\frac{1}{\sqrt{1}+\sqrt{2}}+\frac{1}{\sqrt{2}+\sqrt{3}}+...+\frac{1}{\sqrt{n-1}+\sqrt{n}}=11\)

\(\Leftrightarrow-1+\sqrt{2}-\sqrt{2}+\sqrt{3}-...-\sqrt{n-1}+\sqrt{n}=11\)

\(\Leftrightarrow\sqrt{n}-1=11\Leftrightarrow\sqrt{n}=12\Leftrightarrow n=144\)

Answer 2

mìh ghi thiếu nha = 11 ở đằng sau nha