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:CAT 2017 Slot 2If a1=12×5,a2=15×8,a3=18×11\mathrm{a}_{1}=\frac{1}{2 \times 5}, \mathrm{a}_{2}=\frac{1}{5 \times 8}, \mathrm{a}_{3}=\frac{1}{8 \times 11}a1=2×51,a2=5×81,a3=8×111, then a1,+a2,+a3,+…..a100\mathrm{a}_{1,}+\mathrm{a}_{2,}+\mathrm{a}_{3,}+\ldots . . \mathrm{a}_{100}a1,+a2,+a3,+…..a100 isCAT 2023 Slot 3Let an=46+8na_n = 46 + 8nan=46+8n and bn=98+4nb_n = 98 + 4nbn=98+4n be two sequences for natural numbers n≤100n \le 100n≤100. Then, the sum of all terms common to both the sequences isCAT 2021 Slot 3Consider a sequence of real number x1,x2,x3,...x_1, x_2, x_3, ...x1,x2,x3,... such that xn+1=xn+n−1x_{n+1} = x_n + n - 1xn+1=xn+n−1 for all n≥1n \ge 1n≥1. If x1=−1x_1 = -1x1=−1 then x100x_{100}x100 is equal to