Class 11 Exam  >  Class 11 Questions  >  Prove this :- 41^n - 14^n is a multiple of 27... Start Learning for Free
Prove this :- 41^n - 14^n is a multiple of 27 ?
Most Upvoted Answer
Prove this :- 41^n - 14^n is a multiple of 27 ?
Community Answer
Prove this :- 41^n - 14^n is a multiple of 27 ?
Any number which is a multiple of 27 is in the form of-->
any natural number ×27,
let p(n):41^n-14^n=27d,where d belongs to natural number,
for n=1,
L.H.S=41¹-14¹=41-14=27=27×1=R.H.S,
hence L.H.S=R.H.S so, p(n) is true for n=1,
assume that p(k) is true,
p(k)=41^k-14^k=27 m ,where m belongs to natural number,----(1).
we will prove that p(k+1) is true,
p(k+1),
LHS= 41^(k+1)-14^(k+1),
=41^k.41^1-14^k.14^1,
from (1).41^k=27m+14^k,
=41(27m+14^k)-14^k.14^1,
=41.27m+41.14^k-14^k.14^1,
=41.27m+14^k(41-14),
=41.27m +14^k(27),
=(27)(27m+14^k)=27r,
where r =27m+14^k,
so, p(k+1) is true whenever p(k) is true,
so, by the principle of Mathematical Induction p(n) is true for 41^n-14^n is a multiple of 27.
Explore Courses for Class 11 exam
Question Description
Prove this :- 41^n - 14^n is a multiple of 27 ? for Class 11 2025 is part of Class 11 preparation. The Question and answers have been prepared according to the Class 11 exam syllabus. Information about Prove this :- 41^n - 14^n is a multiple of 27 ? covers all topics & solutions for Class 11 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Prove this :- 41^n - 14^n is a multiple of 27 ?.
Solutions for Prove this :- 41^n - 14^n is a multiple of 27 ? in English & in Hindi are available as part of our courses for Class 11. Download more important topics, notes, lectures and mock test series for Class 11 Exam by signing up for free.
Here you can find the meaning of Prove this :- 41^n - 14^n is a multiple of 27 ? defined & explained in the simplest way possible. Besides giving the explanation of Prove this :- 41^n - 14^n is a multiple of 27 ?, a detailed solution for Prove this :- 41^n - 14^n is a multiple of 27 ? has been provided alongside types of Prove this :- 41^n - 14^n is a multiple of 27 ? theory, EduRev gives you an ample number of questions to practice Prove this :- 41^n - 14^n is a multiple of 27 ? tests, examples and also practice Class 11 tests.
Explore Courses for Class 11 exam
Signup to solve all Doubts
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
10M+ students study on EduRev