Given-f-x-4x-4x-2-1-2x-1-2x-1-Find-the-value-of-f-13-f-14-f-15-f-112-

Question Number 54641 by Joel578 last updated on 08/Feb/19

Given

f (x) = \frac{4 x + \sqrt{4 x^{2} - 1}}{\sqrt{2 x + 1} - \sqrt{2 x - 1}}

Find the value of

f (13) + f (14) + f (15) + \dots + f (112)

Commented by Meritguide1234 last updated on 08/Feb/19

f (x) = \frac{(2 x - 1) + (2 x + 1) + \sqrt{(2 x + 1) (2 x - 1)}}{\sqrt{2 x + 1} + \sqrt{2 x - 1}}

\Rightarrow f (x) = denominator should be positive

\Rightarrow f (x) = \frac{{(\sqrt{2 x - 1})}^{3} - {(\sqrt{2 x + 1})}^{3}}{2}

f (13) + f (14) + \dots + f (112) = 1625