Verified answer

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

1/(15*16) = 1/15 - 1/16 ,,,,,,,,,

1/(15*16)+1/(16*17)+1/(17*18)+1/(18*19)+1/(19*20)= 1/15 - 1/16 + 1/16 - 1/17 + 1/17 - 1/18 + 1/18 - 1/19 + 1/19 - 1/20 = 1/15 - 1/20 = 4/60 - 3/60 = 1/60