chrishello08
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The terms of a sequence are given by T1=1 and Tn = square root (2 + Tn-1) n =2,3,4 Us the method of mathematical induction to show that Tn< 2 for n> and equal to 1
Why is it in the working out the inequality and equality signs alternate in bold
Prove true for n = 1
1<2
therefore true for n = 1
Assume true for n = k
Tk < 2
square root (2 + Tk-1) < 2
Prove true for n = k + 1
T(k+1) < 2square root (2 + Tk) = square root (2 + square root (2 + Tk-1))
< square root (2 + 2)
= 2 (why cant it be < 2)
Why is it in the working out the inequality and equality signs alternate in bold
Prove true for n = 1
1<2
therefore true for n = 1
Assume true for n = k
Tk < 2
square root (2 + Tk-1) < 2
Prove true for n = k + 1
T(k+1) < 2square root (2 + Tk) = square root (2 + square root (2 + Tk-1))
< square root (2 + 2)
= 2 (why cant it be < 2)