Question

найдите натуральное значение х,удовлетворияющее условию! 40 баллов!
(16 задание)

Answer 1

2/n(n + 2) = (n + 2 - n)/n(n + 2) = 1/n - 1/(n + 2)

2/7*9 = (9 - 7)/7*9 = 1/7 - 1/9 итд

2/7*9 + 2/9*11 + .... + 2/x(x + 2) = 1/7 - 1/9 + 1/9 - 1/11 + ....+ 1/(x - 2) - 1/x + 1/x - 1/(x + 2) = 1/7 - 1/(x + 2)

1/7 - 1/(x + 2) = 2/21

1/(x + 2) = 1/7 - 2/21 = 3/21 - 2/21 = 1/21

1/(x + 2) = 1/21

x + 2 = 21

x = 19