Sum of n terms of the series `1/(1.2.3.4.)+1/(2.3.4.5) +1/(3.4.5.6)+....`

FInd the sum of infinite terms of the series (1)/(1.2.3)+(1)/(2.3.4)+(1)/(3.4.5)....

Find the nth term and the sum of n terms of the series 1.2.4+2.3.5+3.4.6+....

If the sum of n term of the series (5)/(1.2.3) + (6)/(2.3.4) + ( 7)/(3.4.5)+"…." is a/2 - (n+b)/((n+1)(n+2)) , then

Find the sum of n terms \ of the series: 1/(1. 2)+1/(2. 3)+1/(3. 4)+...............+1/(n.(n+1))

Sum of n terms of the series (1^(4))/(1.3)+(2^(4))/(3.5)+(3^(4))/(5.7)+…. is equal to

Find the sum to n terms of the series 1.2.3+2.3.4+3.4.5+…