Question

If $x_1,x_2,.....,x_n$ are any real number and $n$ is any positive integer, then ?

• A. $n{\sum }_{i=1}^n{x}_i^2<{\left({\sum }_{i=1}^n{x}_i\right)}^2$
• B. $n{\sum }_{i=1}^n{x}_i^2\ge {\left({\sum }_{i=1}^n{x}_i\right)}^2$
• C. $n{\sum }_{i=1}^n{x}_i^2\ge n{\left({\sum }_{i=1}^n{x}_i\right)}^2$
• D. $Noneoftheabove$

Answer 1

The correct option is B $n{\sum }_{i=1}^n{x}_i^2\ge {\left({\sum }_{i=1}^n{x}_i\right)}^2$

since x1 x2 and xn are positive real numbers

using the nth power mean equality