Nth term of A.G.P

Q. The sum of $1+\frac{2}{5}+\frac{3}{5^2}+\frac{4}{5^3}+.......$ upto n terms is
[MP PET 1982]

1. $\frac{25}{16}-\frac{4n+5}{16\times 5^{n-1}}.$
2. $\frac{3}{7}-\frac{3n+5}{16\times 5^{n-1}}.$
3. $\frac{1}{2}-\frac{5n+1}{3\times 5^{n+2}}.$
4. $\frac{3}{4}-\frac{2n+5}{16\times 5^{n+1}}.$

Q. The sum of the series $1+2x+3x^2+4x^3+.....$ upto n terms is

1. $\frac{1-(n+1)x^n+n{x}^{n+1}}{(1-x{)}^2}$
2. $\frac{1-x^n}{(1-x}$
3. $x^{n+1}$
4. None of these

Q. The sum of the first n terms of the series $\frac{1}{2}+\frac{3}{4}+\frac{7}{8}+\frac{15}{16}+.....$ is
[IIT 1988; MP PET 1996; RPET 1996, 2000; Pb. CET 1994; DCE 1995, 96]

1. $1-2^{-n}$
2. $n+2^{-n}-1$
3. $2^n-1$
4. $2^n-n-1$