Question

Sum of series:1+2+3+..........+n is(a) n(

Answer 1

Answer:

n(n+1)/2 is the answer for the given problem

Answer 2

Answer:

Sum of series = n(n+1) / 2

Step-by-step explanation:

We know that sum of n-terms is given by,

$\boxed{S_{n} = \frac{n[2a + (n-1)d]}{2} }$

From the arithemetic progression given here,

AP -----> 1, 2, 3, ............ n

we get,

First term = a = 1

Common difference = d = 1

Putting these values in the equation of sum of n-terms we get

${S_{n} = \frac{n[2a + (n-1)d]}{2} }$

$S_{n} = \frac{n[2*1 + (n-1)*1]}{2}$

$S_{n} = \frac{n(2+n-1)}{2}$

$S_{n} = \frac{n(n+1)}{2}$