Not sure about the first one .....but....for the second one
We have a same degree polynomial . same degree polynomial situation....so.....the limit of nth term as x becomes increasingly large is just the ratio of the coefficients on the highest power terms in the numerator and denominator....so we have
8 / 6 =
4 / 3
For the first one, note that the term 3n5/(4n5 + 1) gets very close to 3/4 by the time n has reached 10 or so. What that means is that the sum consists of an infinite number of values that are all very nearly 3/4. Adding an infinite number of 3/4 results in an infinite sum.