Do the following question with Principle of Mathematical Induction?

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Answer 1 · 2017-12-05T17:02:52

See below.

In #color(blue)(blue)# is represented #2^n# and in #color(red)(red)# is represented #n^2#

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Now, for #n = 5# is true. Assuming it is true for #n = m# or

#m^2 < 2^m# then

#(m+1)^2 = m^2+2m+1 < 2^m+2^m# or

#2m+1 < 2^m #

but for #m ge 5 rArr 2m+1 < m^2# so the assertion is true for #n ge 5#