Question

How do you find the 5-th partial sum of the infinite series `sum_(n=1)^oo1/(n(n+2)` ?

Answer 1

This is simply the sum of the first 5 terms, so we have
#S_5=1/{1(1+2)}+1/{2(2+2)}+1/{3(3+2)}+1/{4(4+2)}+1/{5(5+2)} =1/3+1/8+1/15+1/24+1/35approx0.6#.