Question

The series 1² + 2² + 3² +4² + ... + 10² is equal to​

Answer 1

Answer:

Sum of squares of first n odd natural numbers =  

n(4n² - 1)

3

Sum of squares of first n even natural numbers =  

2

n(n + 1)(2n + 1)

3

Hence, S =  

5(4 × 5 × 5 - 1)

-  

2

× 5(5 + 1) (2 × 5 + 1)

3 3

S =  

5 × 99

=  

2 × 30 × 11

3 3

Therefore , S = 165 – 220 = – 55

Answer 2

Answer:

1² + 2² + 3² +4² + ... + 10=385.

Step-by-step explanation:

1² + 2² + 3² +4² + ... + 10²

Addition of square of no is given by formulae [n(n+1)(2n+1)/6]

Now put the value of n =10

We get the value of following eq

[n(n+1)(2n+1)/6]=[10×11×21/6]=385