Question

(i) [1/ (1+ √2)] + [1/ ( √2+√3)] + [1/ ( √3+ √4)] + [1/ ( √4+ √5)]​

Answer 1

Answer:

$\sqrt 5 - 1$

Step-by-step explanation:

$\frac {1-\sqrt2}{1-2}+\frac{\sqrt 2-\sqrt 3}{2-3}+\frac{\sqrt 3- \sqrt 4}{3-4}+\frac {\sqrt 4-\sqrt 5}{4-5}$

$=\sqrt 2-1+\sqrt 3-\sqrt 2+\sqrt 4-\sqrt 3+\sqrt 5-\sqrt 4$

$=\sqrt 5 - 1$