Prove that n2 - n is …
CBSE, JEE, NEET, CUET
Question Bank, Mock Tests, Exam Papers
NCERT Solutions, Sample Papers, Notes, Videos
Posted by Daksh Kumar 6 years, 6 months ago
- 1 answers
Test
Related Questions
Posted by Hari Anand 6 months, 1 week ago
- 0 answers
Posted by Parinith Gowda Ms 3 months, 2 weeks ago
- 1 answers
Posted by Lakshay Kumar 1 year, 1 month ago
- 0 answers
Posted by Kanika . 1 month ago
- 1 answers
Posted by Parinith Gowda Ms 3 months, 2 weeks ago
- 0 answers
Posted by Vanshika Bhatnagar 1 year, 4 months ago
- 2 answers
Posted by Sahil Sahil 1 year, 4 months ago
- 2 answers
myCBSEguide
Trusted by 1 Crore+ Students
Test Generator
Create papers online. It's FREE.
CUET Mock Tests
75,000+ questions to practice only on myCBSEguide app
Sia ? 6 years, 6 months ago
Any positive integer is of the form 2q or 2q + 1, for some integer q.
{tex}\therefore{/tex} When n = 2q
{tex}\style{font-family:Arial}{n^2\;-\;n\;=\;n(n\;-\;1)\;=\;2q(2q\;-\;1)=\;2m,}{/tex}
where m = q(2q - 1) ( m is any integer)
This is divisible by 2
When n = 2q + 1
{tex}\style{font-family:Arial}{\begin{array}{l}n^2\;-\;n\;=\;n(n\;-\;1)\;=\;(2q\;+\;1)(2q+1-1)\\=2q(2q+1)\end{array}}{/tex}
= 2m, when m = q(2q + 1) ( m is any integer)
which is divisible by 2.
Hence, n2 - n is divisible by 2 for every positive integer n.
0Thank You