Sum of first n odd natural numbers | 1 + 3 + 5 + … + (2n - 1) | Summation of first n odd numbers

In this video, we will learn derivation of closed form of the sum of first n odd natural numbers.

To derive the closed form of 1 + 3 + 5 + … + (2n - 1), we will apply the closed from of sum of first n natural numbers. Link of the video explaining the derivation of closed from of 1 + 2 + 3 + … + n is given below:

There are at least two ways of finding the summation of first n odd numbers. Here I have explained one.

[ThePulluri]

thank you sir I appreciate the explanation.

[AA-qonw]

1st he's adding all the numbers till 2n then subtracting all even number till 2n . Then you will be left with sum of all the odd numbers till 2n .

[anmolramgiri]

I have a less complex way.

Sum of n terms is (first + last term)/2 x n.
1+(2n-1)/2 x n
nxn
n square

[arindamn]

2:12 why in the 2nd term, the '2n' is missing?

[MuhammadAsghar-vlfq]

Mr Ravi Ranjan solve the following for me
1^2+2^2+3^2+...+(n-1)^2<n^4/4

[sreejitachowdhury]

Thank you sir. Really good explanation!