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

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- May 27th 2007, 07:19 AMpolymerasemathematical induction recursion
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

- May 27th 2007, 08:18 AMSoroban
Hello, polymerase!

I'll help you with part (a) . . .

Quote:

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.