Question

Find the sum of 1/2015+2/2015+3/2015.....+2014/2015​

Answer 1

Answer:2029105/2015=1007

Step-by-step explanation:

Answer 2

The sum of given sequence is 1007

Step-by-step explanation:

To find: The sum of $\dfrac{1}{2015} +\dfrac{2}{2015} +\dfrac{3}{2-15}+.......+ \dfrac{2014}{2015}$

Now taking  $\dfrac{1}{2015}$ common with the given sequence we get

$\dfrac{1}{2015} (1+2+3+........+2014)$

As we know the sum of the series is given by $1+2+3+4+5+....................+n= \dfrac{n(n+1)}{2}$

Therefore we have

$\dfrac{1}{2015} (1+2+3+........+2014)\\\\=\dfrac{1}{2015}(\dfrac{2014(2014+1)}{2} )\\\\=\dfrac{1}{2015}\times \dfrac{2014\times 2015}{2} \\\\=1007$

Hence, the sum of given sequence is 1007

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