Find the sum:
50^2 - 49^2 + 48^2 - 47^2 + ... + 2^2 -1^2
Hello, ceasar_19134!
The sum of the first n squares is given by: .n(n + 1)(2n + 1)/6Find the sum: .50² - 49² + 48² - 47² + ... + 2² - 1²
The sum of all the squares to 50 is: .(50)(51)(101)/2 .= .42,925
Consider the sum of the even squares: .2² + 4² + 6² + ... + 50²
. . = .2²(1² + 2² + 3² + ... + 25²) .= .4·(25)(26)(51)/6 .= .22,100
Hence, the sum of the odd squares is: .[all] - [even] .= .42,925 - 22,100 .= .20,825
Therefore: .[even] - [odd] .= .22,100 - 20,825 .= .1275