wiz-icon
MyQuestionIcon
MyQuestionIcon
1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
Question

2.7n+3.5n5 is divisible by 24 for all nϵN.

Open in App
Solution

Let P(n):2.7n+3.5n5 is divisible by 24

For n=1

2.7+3.55=24

It is divisible of 24

P(n) is true for n = 1

Let P(n) is true for n = k, so

2.7k+3.5k5 is divisible by 24

2.7k+3.5k5=24λ .......(1)

We have to show that,

=2.7(k+1)+3.5(k+1)5

=2.7k.7+3.5k.55

=(24λ3.5k+5)7+15.5k5

=24.7λ21.5k+35+15.5k5

=24.7λ6.5k+30

=24.7λ6(5k5)

=24.7λ6(20v)

[Since 5k5 is multiple of 20]

=24(7λ5v)

=24μ

P(n) is true for n = k + 1

P(n) is true for all nϵN by PMI


flag
Suggest Corrections
thumbs-up
0
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
Mathematical Induction
MATHEMATICS
Watch in App
Join BYJU'S Learning Program
CrossIcon