Question

what is the sum of first x odd natural numbers

Answer 1

1=1=1²
1+3=4=2²
1+3+5=9=3²
1+3+5+7=16=4²
1+3+5+7+9=25=5²

So the answer seems to be:
x²

Answer 2

# What is the sum of first x odd natural numbers?

→ The sum of first x natural odd numbers is given by x².

We can also verify it by considering a Example →

E1 - What is the sum of first 4 natural odd numbers?

S1 → As we know our formula , we can calculate it fastly by using x² , So, sum of first 4 natural odd numbers is = 4² = 16

Let's verify it →

First 4 odd numbers are → 1,3,5,7

Sum of 1,3,5 and 7 = 1+3+5+7 = 16 = 4²

So, 4² = 16.

Hence , We have proved that sum of first x natural odd numbers is x².

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