Prove that 5n-1 is divisible by 4 using mathematical induction.

This answer is restricted. Please login to view the answer of this question.

Login Now

Let, p(n) = 5n – 1

Basis Step:

We show, p(1) is true

i.e. p(1) = 51 – 1

= 4 which is divisible by 4

so p(1) is true

Inductive Step:

Suppose for any arbitary value k, p(k) is true

i.e. p(k): 5k – 1 = 4a, where, a is an integer

or, 5k = 4a + 1

Now, we need to show p(k+1) is divided by 4

p(k+1) = 5k+1 – 1

= 5k.5 – 1

= (4a+1).5 -1

= 20a + 5 – 1

= 20a + 4

= 4(5a + 1)

Here, it is divisible by 4

So, by mathematical induction

5n-1 is divisible by 4

If you found any type of error on the answer then please mention on the comment or report an answer or submit your new answer.
Leave your Answer:

Click here to submit your answer.

Discussion
0 Comments
  Loading . . .