National and Regional Contests India Contests India LIMIT 2019 LIMIT 2019 LIMIT Category B Problem 10 sum of 1/(√n+√(n+2)) Problem Statement 1 1 + 3 + 1 3 + 5 + 1 5 + 7 + … + 1 2017 + 2019 = ? \frac1{1+\sqrt3}+\frac1{\sqrt3+\sqrt5}+\frac1{\sqrt5+\sqrt7}+\ldots+\frac1{\sqrt{2017}+\sqrt{2019}}=? 1 + 3 1 + 3 + 5 1 + 5 + 7 1 + … + 2017 + 2019 1 = ? < s p a n c l a s s = ′ l a t e x − b o l d ′ > ( A ) < / s p a n > 2019 − 1 2 <span class='latex-bold'>(A)</span>~\frac{\sqrt{2019}-1}2 < s p an c l a ss = ′ l a t e x − b o l d ′ > ( A ) < / s p an > 2 2019 − 1 < s p a n c l a s s = ′ l a t e x − b o l d ′ > ( B ) < / s p a n > 2019 + 1 2 <span class='latex-bold'>(B)</span>~\frac{\sqrt{2019}+1}2 < s p an c l a ss = ′ l a t e x − b o l d ′ > ( B ) < / s p an > 2 2019 + 1 < s p a n c l a s s = ′ l a t e x − b o l d ′ > ( C ) < / s p a n > 2019 − 1 4 <span class='latex-bold'>(C)</span>~\frac{\sqrt{2019}-1}4 < s p an c l a ss = ′ l a t e x − b o l d ′ > ( C ) < / s p an > 4 2019 − 1 < s p a n c l a s s = ′ l a t e x − b o l d ′ > ( D ) < / s p a n > None of the above <span class='latex-bold'>(D)</span>~\text{None of the above} < s p an c l a ss = ′ l a t e x − b o l d ′ > ( D ) < / s p an > None of the above