# A=2015(1+2+3+.....2014) B=2014(1+2+3+.....2015) Compare A and B ?

Mar 15, 2017

$B$ is greater than $A$

#### Explanation:

Sum of the series $1 + 2 + 3 + 4 + \ldots \ldots \ldots \ldots \ldots + n = \frac{n \left(n + 1\right)}{2}$

Hence $A = 2015 \left(1 + 2 + 3 + 4 + \ldots \ldots \ldots \ldots \ldots + 2014\right)$

= $2015 \times \frac{2014 \times 2015}{2} = 2015 \times 2014 \times \frac{2015}{2}$

and $B = 2014 \left(1 + 2 + 3 + 4 + \ldots \ldots \ldots \ldots \ldots + 2015\right)$

= $2014 \times \frac{2015 \times 2016}{2} = 2015 \times 2014 \times \frac{2016}{2}$

It is evident that $B > A$

Mar 15, 2017

$B > A$
$A - B = 2015 \left(1 + 2 + \cdots + 2014\right) - \left(2014 \left(1 + 2 + \cdots + 2014\right) + 2014 \cdot 2015\right) = - 2014 \cdot 2015$
then if $A - B = - 2014 \cdot 2015 \to B > A$