Use app×
Join Bloom Tuition
One on One Online Tuition
JEE MAIN 2025 Foundation Course
NEET 2025 Foundation Course
CLASS 12 FOUNDATION COURSE
CLASS 10 FOUNDATION COURSE
CLASS 9 FOUNDATION COURSE
CLASS 8 FOUNDATION COURSE
0 votes
665 views
in Combinatorics and Mathematical Induction by (49.1k points)
closed by

Use the principle of mathematical induction to prove that for every natural number n.

(1 + 3/1)(1 + 5/4)(1 + 7/9) ... (1 + (2n + 1)/n2) = (n + 1)2

1 Answer

+1 vote
by (46.9k points)
selected by
 
Best answer

Let P(n) be the given statement, i.e.

⇒ P(1) is true. 

We note than P(n) is true for n = 1. 

Assume that P(k) is true

Now, we shall prove that P(k + 1) is true whenever 

P(k) is true. We have,

∴ P(k + 1) is also true whenever P(k) is true 

Hence, by the principle of mathematical induction, P(n) is also true for all n ∈ N.

Welcome to Sarthaks eConnect: A unique platform where students can interact with teachers/experts/students to get solutions to their queries. Students (upto class 10+2) preparing for All Government Exams, CBSE Board Exam, ICSE Board Exam, State Board Exam, JEE (Mains+Advance) and NEET can ask questions from any subject and get quick answers by subject teachers/ experts/mentors/students.

...