If $a, b, c$ are any three positive numbers,then what is the minimum value of $(a + b + c) \left( \frac{1}{a} + \frac{1}{b} + \frac{1}{c} \right)$?

The product of $n$ positive numbers is unity. Their sum is

If $a, b, c$ are in $A.P.$ and $a^2, b^2, c^2$ are in $H.P.$,then

Let $b_i > 1$ for $i = 1, 2, \ldots, 101$. Suppose $\log _e b_1, \log _e b_2, \ldots, \log _e b_{101}$ are in Arithmetic Progression $(A.P.)$ with the common difference $\log _e 2$. Suppose $a_1, a_2, \ldots, a_{101}$ are in $A.P.$ such that $a_1 = b_1$ and $a_{51} = b_{51}$. If $t = b_1 + b_2 + \cdots + b_{51}$ and $s = a_1 + a_2 + \cdots + a_{51}$,then:

The first term of an arithmetic progression is $1$. If the second,tenth,and thirty-fourth terms form a geometric progression,then the common difference of the arithmetic progression is:

Let $a_1, a_2, a_3$ be any positive real numbers,then which of the following statements is not true?