Question

The least positive integer n for which $\sqrt{n+1}-\sqrt{n-1}<0.2$ is

• A. $24$
• B. $25$
• C. $26$
• D. $27$

Answer 1

The correct option is C $26$

$\sqrt{n+1}-\sqrt{n-1}<0.2\sqrt{n+1}<\sqrt{n-1}+0.2\sqrt{n-1}+0.2>\sqrt{n+1}$

squaring both sides

$n-1+0.04+0.4\sqrt{n-1}>n+10.4\sqrt{n-1}>1.96\sqrt{n-1}>4.9n-1>24.01n>25.01$

So the least positive integral value of $n$ is $26$

Option $C$ is correct.