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Sum of squares of first n natural numbers=n(n+1)(2n+1)/6

Posted by Rishabh Pawar 5 years ago

CBSE > Class 10 > Mathematics

1 answers

Gaurav Seth 5 years ago

To find the sum of squares, we use the formula of (n+1)³ as shown in the picture.

In the proof, I have used one result directly:

1 + 2 + 3 + ... + n = n(n+1)/2

Proof:
Given series is an A.P. with
First term = 1
Last term = n
Number of terms = n

Sum = n/2 [First term + Last Term]
So, Sum = n/2 [1 + n]
So, Sum = n(n+1)/2

That is, 1 + 2 + 3 + ... + n = n(n+1)/2

0Thank You

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CBSE > Class 10 > Mathematics