Question

find the value of 1+2+3........120.

Answer 1

$\orange{\mathfrak{Here is your answer.......Hope this helps you....}}$

Answer 2

This is an Arithmetic Progression,

You can that second term (2) can be obtain by adding 1 to first term (1), Likewise you can take the next term by adding 1 to each term. That is called Arithmetic Progression.

We can use the below equation to find the total/sum of the progression,

$S_{n} = n/2 (a + l)$

a - First term

l - Last term

But before that we have to find which term 120 is, for that we can use the below equation which uses to find the term of an Arithmetic Progression,

$T_{n} = a + (n-1)d$

120 = 1 + (n-1) x 1

120 =1 + (n-1)

n = 120 -1 + 1

n = 120

So 120 is the 120th term of the progression,

Then we can use equation one to find the sum of the progression,

$S_{120}= 120/2 (1+120)$

            = 60 x 121

            = 7260

So the answer is 7260