Question

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

Answer 1

Answer:

4²ⁿ > 15n

Step-by-step explanation:

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

4²ⁿ > 15n

for n = 1

4² > 15

Which hold trues

for n = 2

4⁴ > 15 * 2

=> 256 > 30

let say for n = a it hold true

4²ᵃ > 15a

then

for a + 1

4²⁽ᵃ⁺¹⁾ = 4² * 4²ᵃ   = 16 * 4²ᵃ

> 16 * 15a

> 15 * 15a + 15a

> 15* (15a -1) + 15 + 15a

> 15(a + 1) + 15* (15a -1)

> 15(a + 1)

Hence holds true