Q. 133.7( 76 Votes )
Show that 9n+1 – 8n – 9 is divisible by 64, whenever n is a positive integer.
Answer :
In order to show that 9n+1 – 8n – 9 is divisible by 64,
we have to prove that
9 n+1 – 8n – 9 = 64 k, where k is some natural number
Now,
9n+1 = (1+8)n+1
We know that-
putting a =1, b = 8, and n = n+1
Hence,
Taking out (8)2 from right side, we get-
where is a natural number
Thus, 9n+1 – 8n – 9 is divisible by 64.
Hence Proved.
Rate this question :
How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Related Videos
Quiz on Greatest term in binomial expansion | Revising Binomial theorem38 mins
Binomial theorem for any index | Interactive Quiz48 mins
Greatest term in binomial expansion | Revising Binomial theorem43 mins
Finding remainder using binomial theorem43 mins
Finding coefficient of x^n in binomial expansion59 mins
Interactive Quiz on Binomial Theorem40 mins
Lecture on properties of Binomial Coefficients58 mins
Interactive Quiz on properties of Binomial Coefficients51 mins
Master on Binomial Theorem for any index41 mins
Interactive Quiz | general & middle terms53 mins




















Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
view all courses
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation


RELATED QUESTIONS :
Prove that
Using binominal theorem, evaluate each of the following :
(i) (101)4 (ii) (98)4
(iii)(1.2)4
RS Aggarwal - Mathematics
Evaluate :
RS Aggarwal - Mathematics
Using binomial theorem, expand each of the following:
(3x2 – 2ax + 3a2)3
RS Aggarwal - Mathematics