Hello, ceasar_19134!

The sum of the firstFind the sum: .50² - 49² + 48² - 47² + ... + 2² - 1²nsquares is given by: .n(n + 1)(2n + 1)/6

The sum ofallthe squares to 50 is: .(50)(51)(101)/2 .= .42,925

Consider the sum of theevensquares: .2² + 4² + 6² + ... + 50²

. . = .2²(1² + 2² + 3² + ... + 25²) .= .4·(25)(26)(51)/6 .= .22,100

Hence, the sum of theoddsquares is: .[all] - [even] .= .42,925 - 22,100 .= .20,825

Therefore: .[even] - [odd] .= .22,100 - 20,825 .= .1275