Question

Find the sum of every counting number from 1 to 63 inclusive.

i.e. 1+2+3+4+ ... +62+63 = ?

Also explain a mathematical method that can be used to shorten this problem from one of adding 63 individual values.

Answer 1

Answer:

2016

Step-by-step explanation:

To find out the sum of the terms, we can use the concept of arithmetic progression.

To find out the sum of the terms, we use the formula:

$S_{n} = \frac{n}2[a + l]$

Where,

n = Number of terms

a = First term of the sequence

l = Last term of the sequence

So, we can say that,

n = 63

a = 1

l = 63

Substituting the values stated into the formula,

$S_{63} = \frac{63}2[1 + 63]$

     $= \frac{63}2 [64]$

      = 63 × 32

      = 2016