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

a1=2

a2=2 1/2

a3=3 1/3

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!