Funny Yet Cool Trick Which You Probably Never Noticed
Let me ask you a Question : Why Did Kattapa Kill Bahubali ??
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Okay Jokes Apart ........And Besides Everyone Now Knows The Answer.
HERE'S THE REAL QUESTION : :
What is the sum of the first 13 positive odd numbers?
A big hint:
SOLUTION :
Correct answer: 169
The sum of the first odd numbers is
A visualization of this claim:
Therefore, the sum of the first 13 odd numbers is 13^2 = 169
A Quick Proof:
Consider that the positive even numbers are those of the form 2n , where n can be any positive integer, starting with 1 . Similarly, the odd numbers are, in turn, numbers of the form 2n - 1 , again where n can be any positive integer, starting with 1.
Here is a quick inductive proof that the sum of the first odd numbers is :
Observe that (n - 1)^2 + (2n +1) = n^2 . Since 2n + 1 is the nth odd number, if the statement is true for n , it's now proven to also be true for n + 1. Clearly, the statement holds true for n = 1 , so that can be our base case. And inductive reasoning takes over from there!
PS : THIS PROOF HAS COSTED ME DEARLY .......................... I LOST SOMEONE SPECIAL OWNING TO THIS...................
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