The product of $$n$$ positive numbers is 1. Their sum is
A.
a positive integer
B.
divisible by $$n$$
C.
equal to $$n + \frac{1}{n}$$
D.
greater than or equal to $$n$$
Answer :
greater than or equal to $$n$$
Solution :
$$\eqalign{
& A = \frac{{{a_1} + {a_2} + ..... + {a_n}}}{n},G = \root n \of {{a_1}{a_2}.....{a_n}} = 1; \cr
& A \geqslant G \cr
& \Rightarrow \,\,{a_1} + {a_2} + ..... + {a_n} \geqslant n. \cr} $$
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-