Readers do you see a pattern in numbers? Can you go and check these out, my discovery.
Did you know the sum of any number of odd numbers in order is the square of the number? That is sum of first 5 odd numbers is 25. You can calculate any number of sum of odd numbers with this , cool right!
Sum of even numbers is n*n+1 where n is the number of even numbers. Cool finding!
For your information zero is neither odd or even, I’m excited to find more patterns.
Farmers can sow their seeds and can calculate their output using this I think , not sure of other applications.
Do you think of any more such things? Let me know.
3 thoughts on “Formulas…cool finding!”
hi Abhi, cool post. I think you’ve just stumbled upon arithmetic progressions. And just maybe touched the concept of mathematical induction. Both pretty cool to discover for yourself.
The sum of n-numbers is n*(n+1)/2. This is the classic “summation” formula.
I don’t buy your odd number formula though (try again?).
Your odd number formula is actually correct. I stand corrected!
Using the summation formula, sum of first n numbers, lets call it Sum(1,2,..n) = n*(n+1)/2, you can derive sum of odd and even numbers as follows:
First n even numbers are 2*k, where k=1,2,3,…n
Therefore, sum(2*k) = 2*sum(k) = 2*sum(k=1,2,3…n)=2*n*(n+1)/2 = n*(n+1)
First n odd numbers is 2*k-1, where k=1,2,3…n
therefore, sum(2*k-1) =2*sum(k)-sum(1)=2*sum(1,2,3…n) – sum(1) = 2*n*(n+1)/2 – n = n^2
Say this is really interesting. Some finding leading to more patterns and derivatives.arithmetic expressions are awesome.