Question

Using mathematical induction prove that for any natural number n, 4^2n >15n

Answer 1

To prove for any natural number n 42 n > 15 n

step 1: Let n=1 that is a ntural number let us check the given condition

then

42(1)>15(1)

42>15

which is true

Step 2 : Let k be a natural number then

it should be proved when n=k

by the rule

if k is a natural number then

42 k >15 k

step 3:

As k is natural number so (n=k+1) is also a natural Number

so

by mathematical induction

42(k+1)>15(k+1)

42k + 42 > 15 k + 15

42 k + 42 -15 >15k +15-15

42 K + 27 > 15 k (for all k=n)