Преобразуйте сумму к более простому виду 1 / 1 * 2 + 1 / 2*3+1/3*4+...+1/n (n+1)

1/(1 * 2) + 1/(2 * 3) + 1/(3 * 4) + ... + 1/(n * (n + 1)) =

= (2 – 1)/(1 * 2) + (3 – 2)/(2 * 3) + (4 – 3)/(3 * 4) + ... + ((n + 1) – n)/(n * (n + 1)) =

= (1 – ½) + (1/2 – 1/3) + (1/3 – ¼) + ... + (1/n – 1/(n + 1)) =

= 1 – 1/(n + 1) = (n + 1 – 1)/(n + 1) = n/(n + 1).