Suppose a1=12−12,a2=23−13,a3=34−14,a4=45−15,a5=56−16. a) Find an explicit formula for an: . b) Determine whether the sequence is convergent or divergent: . (Enter "convergent" or "divergent" as appropriate.)

I'm going to assume you meant to write fractions (because if [tex]a_n[/tex] are all non-negative integers, the series would clearly diverge), so that[tex]a_1=\dfrac12-\dfrac12[/tex][tex]a_2=\dfrac23-\dfrac13[/tex][tex]a_3=\dfrac34-\dfrac14[/tex]and so on.a. If the pattern continues as above, we would have the general term[tex]a_n=\dfrac n{n+1}-\dfrac1{n+1}=\dfrac{n-1}{n+1}[/tex]b. Note that we can write [tex]a_n[/tex] as[tex]a_n=\dfrac{n-1}{n+1}=\dfrac{n+1-2}{n+1}=1-\dfrac2{n+1}[/tex]The series diverges by comparison to the divergent series[tex]\displaystyle\sum_{n=1}^\infty\frac1n[/tex]