CATAlgebra > Hardn−1a1+an\frac{n-1}{\sqrt{a_{1}}+\sqrt{a_{n}}}a1+ann−1na1−aa+1\frac{\mathrm{n}}{\sqrt{\mathrm{a}_{1}}-\sqrt{\mathrm{a}_{\mathrm{a}+1}}}a1−aa+1nn−1a1+a2−1\frac{n-1}{\sqrt{a_{1}}+\sqrt{a_{2-1}}}a1+a2−1n−1na1+an+1\frac{n}{\sqrt{a_{1}}+\sqrt{a_{n+1}}}a1+an+1n✅ Correct Option: 4Related questions:CAT 2023 Slot 1For some positive and distinct real numbers x,yx, yx,y and zzz, if 1y+z\frac{1}{\sqrt{y}+\sqrt{z}}y+z1 is the arithmetic mean of 1x+z\frac{1}{\sqrt{x}+\sqrt{z}}x+z1 and 1x+y\frac{1}{\sqrt{x}+\sqrt{y}}x+y1, then the relationship which will always hold true, isCAT 2023 Slot 3The value of 1+(1+13)14+(1+13+19)116+(1+13+19+127)164+……1+\left(1+\frac{1}{3}\right) \frac{1}{4}+\left(1+\frac{1}{3}+\frac{1}{9}\right) \frac{1}{16}+\left(1+\frac{1}{3}+\frac{1}{9}+\frac{1}{27}\right) \frac{1}{64}+\ldots \ldots1+(1+31)41+(1+31+91)161+(1+31+91+271)641+……, isCAT 2023 Slot 1A lab experiment measures the number of organisms at 888 am every day. Starting with 222 organisms on the first day, the number of organisms on any day is equal to 333 more than twice the number on the previous day. If the number of organisms on nth day exceeds one million, then the lowest possible value of nnn is