Question 81 it's due tomorrow it's very important i need to know it me

Find the sum of the first 8 terms of the following sequence. round to the nearest hundredth if necessary.

Can someone check if i did this correct. it’s number 4 if you’re wondering.

Is the product of two rational numbers irrational or rational? first, make a hypothesis by multiplying two rational numbers. then, use variables such as x=a/b and y=c/d and the closure property of integers to prove your hypothesis.