Calculate the square of 1 - the square of 2 + the square of 3 - the square of 4 + the square of 19 - the square of 20

Calculate the square of 1 - the square of 2 + the square of 3 - the square of 4 + the square of 19 - the square of 20

Square of 1-2 + square of 3-4 + square of 19-20
=(2) + (2) + (2) + (2) + (2) + (2) + (2) + (2) + (2) + (2) + (2) + (2) + (2) + (2) + (2) + (2) + (2) + (2) + (2) + (2) + (2) + (2) + (2) + (2) + (2) + (2) + (2) + (2) + (2) + (2) + (2) + (2) + (2) + (2
= (2+1)(1-2)+ (4+3)(3-4)+...(20+19)(19-20)
= -3+-7+-11+.+-39
=-(3+39)*10/2
=- 210

What is the square of 1 * 2 + 2 * 3 + 3 * 4 +. + 19 * 20?

an = n(n+1)^2 = n(n+1)(n+2) -n(n+1) =(1/4)[n(n+1)(n+2)(n+3)-(n-1)n(n+1)(n+2)] - (1/3)[n(n+1)(n+2) -(n-1)n(n+1)]Sn = a1+a2+...+an =(1/4)n(n+1)(n+2)(n+3) - (1/3)n(n+1)(n+2)1.2^2+2.3^2+...+...

62ab427 is a multiple of 99, finding a, B

A = 2, B = 4, because 99 is a multiple of 9, the multiple of 9 has a characteristic, that is, the sum of each digit, and then add up, the final result must be 9, according to this result, it is not difficult to calculate: 6 + 2 + A + B + 4 + 2 + 7 = 21 + A + B, and a, B are natural numbers less than 10, the sum will not exceed 19, because the result of a + B can only