How do I prove by induction,
If t1 = 1, tn+1 = 1 + Ö(1 + tn) prove a) tn < 3 for all n Î N
b) tn+1 > tn for all n Î N
Hello, polymerase!
I'll help you with part (a) . . .
If , prove by induction:
a) for all
Verify . . Is
. . . . . yes!
Assume is true: .
Add 1 to both sides: .
Take the square root of both sides: .
Add 1 to both sides: .
Therefore: .
. . The inductive proof is complete.