Let Tn by defined by:

T(0) = 1

T(1) = x

T(n+1) = 2x(Tn) - (Tn-1) NOTE:[the n-1 is small, you know?]

a) Use induction to show that Tn is a polynomial of degree n for all n.

b) Use induction to show that Tn(1) = 1 for all n.

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- Aug 15th 2010, 11:14 PMbrumby_3Induction question, help greatly appreciated :)
**Let Tn by defined by:**

T(0) = 1

T(1) = x

T(n+1) = 2x(Tn) - (Tn-1) NOTE:[the n-1 is small, you know?]

a) Use induction to show that Tn is a polynomial of degree n for all n.

b) Use induction to show that Tn(1) = 1 for all n. - Aug 16th 2010, 12:58 AMVlasev
for a you have your base case(s) already since T(0) is of degree 0 and T(1) is of degree 1. Now you might as well use the strong principle, that is assume that the statement is true for all k between 2 and n. Then use the recurrence relation to show that it is true for T(n+1) and you are done. It is the same for b).