The sum of 0.2 + 0.004 + 0.00006 + 0.0000008 + . . . . . to $$\infty $$ is
A.
$$\frac{{200}}{{891}}$$
B.
$$\frac{{2000}}{{9801}}$$
C.
$$\frac{{1000}}{{9801}}$$
D.
None of these
Answer :
$$\frac{{2000}}{{9801}}$$
Solution :
Sum $$ = \frac{2}{{10}} + \frac{4}{{{{10}^3}}} + \frac{6}{{{{10}^5}}} + \frac{8}{{{{10}^7}}} + .....\,{\text{to }}\infty $$ which is an arithmetico-geometric series
Releted MCQ Question on Algebra >> Sequences and Series
Releted Question 1
If $$x, y$$ and $$z$$ are $${p^{{\text{th}}}},{q^{{\text{th}}}}\,{\text{and }}{r^{{\text{th}}}}$$ terms respectively of an A.P. and also of a G.P., then $${x^{y - z}}{y^{z - x}}{z^{x - y}}$$ is equal to:
If $$a, b, c$$ are in G.P., then the equations $$a{x^2} + 2bx + c = 0$$ and $$d{x^2} + 2ex + f = 0$$ have a common root if $$\frac{d}{a},\frac{e}{b},\frac{f}{c}$$ are in-