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

For all integers n1, which of the following is divisible by 9?

A
8n+1
No worries! We‘ve got your back. Try BYJU‘S free classes today!
B
4n3n1
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
C
32n+3n+1
No worries! We‘ve got your back. Try BYJU‘S free classes today!
D
10n+1
No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution

The correct option is B 4n3n1
A) a(n)=8n+1=(91)n+1=9nnC19n1+..+(1)n1nCn19+(1)nnCn+1
a(n)=9(9n1nC19n2+..+(1)n1nCn1)+(1)nnCn+1=9λ+(1)nnCn+1
if n is even, then a(n)=9λ+2 which is not divisible by 9
if n is odd, then a(n)=9λ which is divisible by 9
B) b(n)=4n3n1=(3+1)n3n1=3n+nC13n1+...+nC232+nC13+nCn3n1
b(n)=9(3n2+nC13n3+...+nC2)=9λ
Therefore, b(n) is divisible by 9.
C)
c(n)=32n+3n+1=3(32n1+n)+1=3λ+1
Therefore, c(n) is not divisible by 9.
D)
d(n)=10n+1=(9+1)n+1=9n+nC19n1+...+nCn+1
d(n)=9(9n1+nC19n2+..+nCn1)+2=9λ+2
Therefore, d(n) is not divisible by 9

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