A) 0
B) 1
C) 2
D) 3
Correct Answer: D
Solution :
\[\frac{1}{1+\sqrt{2}}+\frac{1}{\sqrt{2}+\sqrt{3}}+....+\frac{1}{\sqrt{15}+\sqrt{16}}\] On rationalization \[=\frac{1-\sqrt{5}}{1-2}+\frac{\sqrt{2}-\sqrt{3}}{2-3}+...+\frac{\sqrt{15}-\sqrt{16}}{15-16}\] \[=-1[1-\sqrt{2}+\sqrt{2}-\sqrt{3}+...+\sqrt{15}-\sqrt{16}]\] \[=-[1-4]=3\]You need to login to perform this action.
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