Direct sum of squares

Algebra Level 1

What is the value of

$10^2+9^2+8^2+7^2+6^2+5^2+4^2+3^2+2^2+1^2?$

The answer is 385.

21 solutions

Lorenc Bushi
Dec 22, 2013

This sum is of the form: $1^2+2^2+3^2+............+n^2$ , where in this case $n=10$ .The formula to calculate this sum is : $S=\frac{n(n+1)(2n+1)}{6}$ .Substituting $n=10$ we obtain $\boxed{S=385}$

Where on earth did 6 come from? Mind explaining? And what is the formula actually? I thought the formula to calculate sum is n/2 [2a+(n-1)Xd]

Sumaita Ahmed - 7 years, 5 months ago

this is the formula to calculate arithmetic sum of a series

Shakir Khatti - 7 years, 4 months ago

That is formula for an A.P.

Kushagra Sahni - 7 years, 3 months ago

it's just a matter of thinking :)

Jolina Malicdem - 7 years, 4 months ago

When you know the squares up to 10, then we do you not just add them together?

I mean to solve this:

(110*21) / 6

without calculator is much more difficult.

Patrick Engelmann - 7 years, 5 months ago

I think the six came from the way of adding from 1 to any number n- (2n)(n+1)/2- this technique was used similarly in adding up the squares.

Juliet Crome - 7 years, 5 months ago

why six?

Jiggy Gerardo - 7 years, 5 months ago

yah why 6?

kish tolentino - 7 years, 5 months ago

Good solution.................

ashik sunny - 7 years, 5 months ago

where the 6 come from? mind to explain?

Iyvon Teh - 7 years, 5 months ago

is it has a best solution for this question without using a scientific calculator or prediction?can i have it?

Hazarel zairy - 7 years, 5 months ago

is actually very easy. (10X10)+(9X9)+(8X8)+.......(1+1)= 385

Lee KarWee - 7 years, 4 months ago

Simple

Prayogi Aja - 7 years, 4 months ago

ahm .. I think that formula is for the "Sum of the squares of the first n natural numbers".. That's why there's number 6 in there.. It's just in the solution

Lexi Kathlynn Petil - 7 years, 4 months ago

not difficult

DHIWAKAR S - 7 years, 3 months ago

how do you get the formula

aaryan vaishya - 2 years, 5 months ago