Question

вычислите значение выражения 2/3*5+2/5*7+...+2/29*31

Answer 1

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

2/3*5 = 1/3 - 1/5

1/3 - 1/5 + 1/5 - 1/7 + ...... + 1/27 - 1/29 + 1/29 - 1/31 = 1/3 - 1/31 = (31 - 3)/93 = 28/93