For the sequence a1= 1, a(n+1)= 1 + 2a(n)/ 1 + a(n) n=1,2,3,..

we need to show that the sequence is bounded from above by 100.

I talked to my prof and he said to use induction with a(k) < 100 to show a(k+1) < 100.

if I set it up, i get

1 + 2a(k)/ 1+ a(k) < 100

1 + 2a(k) < 100 (1+ a(k))

1 + 2a(k) < 100 + 100 a(k)

-99 < 98 a(k)

which is where I am stuck. How would I use this to show that a(n) is bounded by 100?

Please help!!!