an=n+1/n (btw anything that i write with a less than sign i mean less than or equal to i just cant write it.)
so i figured out that
so my guess is that its increasing.
so for n=k
i need to show ak<ak+1
a1=2<ak=2 1/2 so i showed this right i believe.
next, i need to show that ak+1<ak+2
so i did (k+1)+(1/k+1)<(k+2)+(1/k+2)
cancelled out and reduced to (k+1)+1<(k+2)+1
reduced to (k+1)<(k+2)
reduced to 1<2
is this right to show that it is increasing?
then i just took the limit of n+1/n and got infinity, so it is not bounded.
is this all right? my work and all? my professor did it a different way. Thank you guys!