A.G.P

Q. If |x| < 1, then the sum of the series 1 + 2x + $3x^2$ + $4x^3$ + ....... $\infty$ will be

1. $\frac{1}{1-x}$
2. $\frac{1}{1+x}$
3. $\frac{1}{(1+x{)}^2}$
4. $\frac{1}{(1-x{)}^2}$

Q. The nth term of an Arithmetic geometric progression is given by $[a+(n-1\left)d\right]b{r}^{n-1}$

1. False
2. True

Q. $1+\frac{3}{2}+\frac{5}{2^2}+\frac{7}{2^3}+....\infty$ is equal to
[DCE 1999]

1. 3
2. 6
3. 9
4. 12

Q. The sum of infinite terms of the following series $1+\frac{4}{5}+\frac{7}{5^2}+\frac{10}{5^3}+.......$ will be
[MP PET 1981; RPET 1997; Roorkee 1992; DCE 1996, 2000]

1. $\frac{3}{16}$
2. $\frac{35}{8}$
3. $\frac{35}{4}$
4. $\frac{35}{16}$

Q. If $(10{)}^9+2(11{)}^1(10{)}^8+3(11{)}^2(10{)}^7+\dots \dots +10(11{)}^9=k(10{)}^9$, then k is equal to

1. $100$
2. $\frac{121}{10}$
3. $\frac{441}{100}$
4. $110$

Q.

If p, q, r are in A.P. and x, y, z are in G.P. then $x^{q-r}.y^{r-p}.z^{p-q}$ is equal to

1. 1
   

2. xyz
   

3. p+q+r

4. x+y+z
   

Q. The sum to infinite terms of the series
$1+\frac{2}{3}+\frac{6}{3^2}+\frac{10}{3^3}+\frac{14}{3^4}\cdots$ is

1. 3
2. 4
3. 6
4. 2

Q. The sum of the series $1+2.2+{3.2}^2+{4.2}^3+{5.2}^4+\cdots +{100.2}^{99}$ is

1. ${99.2}^{100}-1$
2. ${100.2}^{100}$
3. ${99.2}^{100}$
4. ${99.2}^{100}+1$

Q. If $S=\sum _{n=0}^{\infty }\frac{2n+3}{3^n}$ then, the value of $S$ is equal to

Q. If $1+2x+3x^2+4x^3+\cdots +\infty \ge 4,$ $(|x|<1)$, then

1. least value of $x$ is $\frac{1}{2}$
2. greatest value of $x$ is $\frac{4}{3}$
3. least value of $x$ is $\frac{2}{3}$
4. greatest value of $x$ deos not exist