Question

Prove by the principle of mathematical induction that

15^2n-1 +1

for all

n N

is a multiple

of 16​

Answer 1

Answer:Let p n : 15 2 n - 1 + 1 is divisible by 16 For n = 1 p 1 : 15 2 - 1 + 1 = 15 + 1 = 16 , which is divisible by 16 So , p n is true for n = 1 Let us assume that p n is true for n = k p k : 15 2 k - 1 + 1 is divisible by 16 15 2 k - 1 + 1 = 16 d For n = k + 1 p k + 1 : 15 2 k + 1 - 1 + 1 = 15 2 k + 2 - 1 + 1 = 15 2 .

Step-by-step explanation: hope it helps