CATAlgebra > Mediumn−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:2025 Slot 2Let ana_nan be the nthn^{th}nth term of a decreasing infinite geometric progression. If a1+a2+a3=52a_1+a_2+a_3 = 52a1+a2+a3=52 and a1a2+a2a3+a3a1=624a_1a_2+a_2a_3+a_3a_1 = 624a1a2+a2a3+a3a1=624, then the sum of this geometric progression isCAT 2019 Slot 2If (2n+1)+(2n+3)+(2n+5)+....+(2n+47)=5280(2n + 1) + (2n + 3) + (2n + 5) + .... + (2n + 47) = 5280(2n+1)+(2n+3)+(2n+5)+....+(2n+47)=5280, then what is the value of 1+2+3+...+n1 + 2 + 3 + ... + n1+2+3+...+n?CAT 2020 Slot 3If x1=−1x_1 = -1x1=−1 and xm=xm+1+(m+1)x_m = x_{m+1} + (m + 1)xm=xm+1+(m+1) for every positive integer m,m,m, then x100x_{100}x100 equals