Question

Tính:

a) N=1x3+5x7+9x11+...+99x101

b) P=1^2+4^2+7^2+....+100^2

Answer 1

A = 1 x 3 + 5 x 7 + 9 x 11 + ... + 99 x 101
6A = 6 x (1 x 3 + 5 x 7 + 9 x 11 + ... + 99 x 101)
6A = 1 x 3 x 6 + 5 x 7 x 6 + 9 x 11 x 6 + ... + 99 x 101 x 6
6A = 1 x 3 x (5 + 1) + 3 x 5 x (7 - 1) + 5 x 7 x (9 - 3) + ⋯ + 99 x 101 x (103 - 97)
6A = 1 x 3 x 1 + 1 x 3 x 5 + 3 x 5 x 7 - 1 x 3 x 5 + 5 x 7 x 9 - 3 x 5 x 7 + ⋯ + 99 x 101 x 103 - 97 x 99 x 101
6A = 1 x 3 x 1 + (1 x 3 x 5) + (3 x 5 x 7) - (1 x 3 x 5) + (5 x 7 x 9 ) - (3 x 5 x 7) + ⋯ + (99 x 101 x 103) - (97 x 99 x 101)
6A = 3 - 99 x 101 x 103 = 1019703
=> A = 1019703/6