CameraIcon
CameraIcon
SearchIcon
MyQuestionIcon
MyQuestionIcon
1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
Question

For every positive integer n, 7n−3n is divisible by 4.

A
True
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
B
False
No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution

The correct option is A True
Consider P(n):7n3n is divisible by 4
Now,

P(1):7131=4

Thus, it is true for n=1
Let p(k) is true for n=K
7k3kisdivisibleby4
Now, prov that P(k+1) is true.

7(k+1)3(k+1)=7(k+1)7.3k+7.3k3(k+1)=7(7k3k)+(73)3k=7(4d)+(73)3k=7(4d)+4.3k=4(7d+3k)

Hence, P(n):7n3n is divisible by 4 is true.

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