Question

Compute the squares of natural numbers from 90 to 100​

Answer 1

Answer:

Square 20 and get 400.

Now double 20, get 40, add that and 1 to the 400 and get 441.

That’s 21 squared.

Now double 21, get 42, add that and 1 to 441 and get 484.

That’s 22 squared.

Repeat until you reach 200 squared.

(which, btw, is 40000)

Now if the OP REALLY meant to ask how to calculate the sum of the squares from 20 to 200 then the problem is different.

The formula for the sum of the FIRST N squares is:

(N * (N + 1) * (2N + 1)) / 6 .

So to find the sum of the squares from 20 to 200 we would subtract the sum of the squares for N = 19 from the sum of the squares for N =200.

(19 * 20 * 39) /6 = 19 * 10 * 13 = 2,470

(200 * 201 * 401)/6 = 100 * 67 * 401 = 2,686,700

2,686,700 - 2,470 = 2,684,230

Answer 2

90×90 = 8,100

100×100 = 10,000

please mark as brilliant