Question

write the sum of odd number by observing the following pattern without using addition. 1+3+5+7=4²=16​

Answer 1

Answer:

1+3+5+7 = 4² = 16

Finding out the sum of odd numbers by observing the pattern without using addition is one of the interesting pattern in Square roots.

The logic used in here :

• The sum of first n odd number is n².

Check here :

1+3+5 = 3² = 9 [sum of first odd numbers]

Likewise we have :

1 = 1² = 1

1+3 = 2² = 4

1+3+5 = 3² = 9

1+3+5+7 = 4² = 16

1+3+5+7+9 = 5² = 25

1+3+5+7+9+11 = 6² = 36

And so on...

Answer 2

Answer:

ANSWER

From 1to 19 there are 10 odd numbers.

So 1+3+5+7+−−−−19=10×10=100