Question 390915
{{{1/2+1/6+1/12+1/20+1/30}}}+...+{{{1/((n-1)n) + 1/(n(n+1))}}}
={{{(1-1/2) + (1/2 -1/3) + (1/3 - 1/4) + (1/4 - 1/5) + (1/5 - 1/6)}}}+...+{{{(1/(n-1) - 1/n) + (1/n - 1/(n+1))}}}
={{{1 -  1/(n+1)}}} because of "telescoping" property.