Question

(a) Find the value of the 100th term in the following sequence of numbers. Jus-tify your answer by describing the pattern that you found and why it works.(1+1/2). (1+1/3), (1+1/4),...

Answer 1

1) In this Sequence, let's rewrite it to better see it.

`\begin{gathered} a_1=\text{ }(1\text{ +}(1)/(2))\text{ =}(3)/(2) \\ a_2=\text{ (}1+(1)/(3)\text{ ) =}(4)/(3)\text{ } \\ a_{3\text{ }=\text{ }}(1+(1)/(4))=(5)/(4) \end{gathered}`

If we subtract we see