No products in the cart.

Prove by pmi that n(n+1)(2n+1) is …

CBSE, JEE, NEET, CUET

CBSE, JEE, NEET, CUET

Question Bank, Mock Tests, Exam Papers

NCERT Solutions, Sample Papers, Notes, Videos

Prove by pmi that n(n+1)(2n+1) is divisible by 6 for all natural numbers

Posted by Nishtha Singal 5 years, 5 months ago

CBSE > Class 11 > Mathematics

1 answers

Saanidhya Kuriyal 5 years, 5 months ago

Let P(n): n(n + 1)(n + 2) is divisible by 6. P(1): 1(1 + 1)(1 + 2) = 6 which is divisible by 6. Thus P(n) is true for n = 1. Let P(k) be true for some natural number k. i.e. P(k): k(k + 1)(k + 2) is divisible by 6. Now we prove that P(k + 1) is true whenever P(k) is true. Now, (k + 1)(k + 2)(k + 3) = k(k + 1)(k + 2) + 3(k + 1)(k + 2) Since, we have assumed that k(k + 1)(k + 2) is divisible by 6, also (k + 1)(k + 2) is divisible by 6 as either of (k + 1) and ( k + 2) has to be even number. P(k + 1) is true. Thus P(k + 1) is true whenever P(k) is true. By principle mathematical induction n(n + 1)(n + 2) is divisible by 6 for all n N.

ANSWER

https://examin8.com

Test

Related Questions

Ch 1 ke questions

Posted by Nitin Kumar 1 year, 4 months ago

CBSE > Class 11 > Mathematics

1 answers

Find the product. (4x²) (–5³)

Posted by Manoj Thakur 1 year, 4 months ago

CBSE > Class 11 > Mathematics

0 answers

Prove that sin square 8x - sin square 3x =sin11x.sin5x

Posted by Sabin Sultana 1 year, 4 months ago

CBSE > Class 11 > Mathematics

0 answers

Square of 169

Posted by Ashish Chaudhary 1 year, 4 months ago

CBSE > Class 11 > Mathematics

1 answers

Express the complex number i-39

Posted by Sana Dharwad 1 year, 4 months ago

CBSE > Class 11 > Mathematics

0 answers

(3+i)x + (1-2i) y +7i =0

Posted by Ananya Sv 1 year, 4 months ago

CBSE > Class 11 > Mathematics

1 answers

Modern ABC class 11 mathematics solutions chapter 2 relation and functions

Posted by Gurleen Kaur 1 year, 4 months ago

CBSE > Class 11 > Mathematics

0 answers

2nC2:nC3=33:10

Posted by K.Y K 1 year, 5 months ago

CBSE > Class 11 > Mathematics

0 answers

The sum of two numbers is 6 time its geometric mean show that numbers are in the ratio (√3 +2): (3-2√2)

Posted by Shubham Jaat 1 year, 4 months ago

CBSE > Class 11 > Mathematics

0 answers

Find the equation of a circle with centre (2,2) and passes through the point (4,5)

Posted by Sethpoulou Apoulou 1 year, 5 months ago

CBSE > Class 11 > Mathematics

0 answers

myCBSEguide App

myCBSEguide

Trusted by 1 Crore+ Students

Test Generator

Test Generator

Create papers online. It's FREE.

CUET Mock Tests

CUET Mock Tests

75,000+ questions to practice only on myCBSEguide app

Google Play

Download myCBSEguide App