Вычислите 1/13*17+1/17*21+...+1/77*81

Question

Вычислите 1/13*17+1/17*21+...+1/77*81

Answer 1

1/13*17 = 1/4 * 4/13*17 = 1/4*(1/13 - 1/17)

1/17*21 = 1/4 * 4/17*21 = 1/4*(1/17 - 1/21)

............

1/77*81 = 1/4 * 4/77*81 = 1/4(1/77 - 1/81)

1/13*17 + 1/17*21 + .... + 1/77*81 = 1/4 * (1/13 - 1/17 + 1/17 - 1/21 + 1/21 - 1/25 +...+ 1/73 - 1/77 + 1/77 - 1/81) = 1/4 * (1/13 - 1/81) = 1/4 * (81 - 13) / 1053 = 1/4 * 68/1053 = 17/1053