Mathematical Induction Inequalities Question (1 Viewer)

[chrishello08]

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)

 

[Trebla]

The equality or inequality follows from the previous line:
.
.
< √(2 + 2)
= 2
.
.
because √(2 + 2) EQUALS 2, and is not less than 2. To say √(2 + 2) < 2 would be incorrect.

 

[chrishello08]

so for the working out to be technically right, it shoudld be written along one line only rather thasn two

 

[chrishello08]

right????

 

[vds700]

so for the working out to be technically right, it shoudld be written along one line only rather thasn two

nah, take a new line for each step as usual

 

[chrishello08]

why does a new line need to be taken i dont get it

 

[chrishello08]

thanks guys i just found out from my sis it is a standard form of simplifying expressions