Question

find the value of 25^26^2+....+50^2.​

Answer 1

Answer: 39013

Step-by-step explanation: 25^2 + 26^2 + 27^2 ... + 50^2

⇒ (38 - 13)^2 + (38 - 12)^2 + (38 -11)^2 ..+ 38^2 ...+(38 + 11)^2 + (38 + 12)^2

Using the formula (x - y)^2 = x^2 - 2xy + y^2 and (x + y)^2 = x^2 + 2xy + y^2 , u will find that all -2xy and +2xy will cancel , but one -2xy will remain (that is the -2xy of (38 - 13)^2 )

Therefore, (38² - 494 + 13²) + (38² + 12²) ..+ 38^2 + ... + (38^2 + 12²)

There are 26 numbers from 25 to 50 , therefore 26(38²) + 2(12² + 11² + 10² .... + 1²) + 13²

⇒ 26 x 1444 + 2(((12 x 13 x 25))/6) + 169 (Used the formula n(n+1)(2n + 1)/6 to find 1^2 + 2^2 + 3^2 .. . + n^2)

⇒ 37544 + 1300 + 169

⇒ 39013

This was one of the tough problems , please mark be brainliest