Question

cum se face?
trebuie aflat n

Answer 1

[tex] \frac{1}{1+ \sqrt{2} } + \frac{1}{ \sqrt{2}+ \sqrt{3} } +...+ \frac{1}{ \sqrt{n} + \sqrt{n+1} } = 10 \\ \\ \text{Prima oara trebuie sa rationalizezi.}\\ \\ \frac{1- \sqrt{2} }{1-2 } + \frac{\sqrt{2}- \sqrt{3}}{ 2-3 } +...+ \frac{\sqrt{n} - \sqrt{n+1} }{n-n-1 } = 10 \\ \\ -(1- \sqrt{2})-(\sqrt{2}- \sqrt{3})-...-(\sqrt{n} - \sqrt{n+1}) = 10 \\ \\ -1+ \sqrt{2}- \sqrt{2}+ \sqrt{3}-...-\sqrt{n} + \sqrt{n+1} = 10 \\ \\ -1+ \sqrt{n+1} = 10 \\ \\ \sqrt{n+1} = 11 \\ \\ n+1 = 121 \\ n = 120[/tex]