Sequences & Series · JEE Main previous year questions

2005 2 questions

1. Q102005 · 28 Apr 2005 · Shift 1

   If $x={\sum }_{n=0}^{\infty }{a}^n,y={\sum }_{n=0}^{\infty }{b}^n,z={\sum }_{n=0}^{\infty }{c}^n$, where a, b, c are in A.P and $|a|<1,|b|<1,|c|<1$ then x, y, z are in

   1. A.G.P.
   2. B.A.P.
   3. C.Arithmetic-Geometric Progression
   4. D.H.P.
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   Answer: D

2. Q602005 · 28 Apr 2005 · Shift 1

   The sum of the series $1+\frac{1}{4.2!}+\frac{1}{16.4!}+\frac{1}{64.6!}+\dots \dots$ ad inf. is

   1. A.$\frac{e-1}{\sqrt{e}}$
   2. B.$\frac{e+1}{\sqrt{e}}$
   3. C.$\frac{e-1}{2\sqrt{e}}$
   4. D.$\frac{e+1}{2\sqrt{e}}$
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   Answer: D