Data Structure
Networking
RDBMS
Operating System
Java
MS Excel
iOS
HTML
CSS
Android
Python
C Programming
C++
C#
MongoDB
MySQL
Javascript
PHP
Physics
Chemistry
Biology
Mathematics
English
Economics
Psychology
Social Studies
Fashion Studies
Legal Studies
- Selected Reading
- UPSC IAS Exams Notes
- Developer's Best Practices
- Questions and Answers
- Effective Resume Writing
- HR Interview Questions
- Computer Glossary
- Who is Who
Find the value of : $\frac{1}{1+a^{n-m}}+\frac{1}{1+a^{m-n}}$.
Given: $\frac{1}{1+a^{n-m}}+\frac{1}{1+a^{m-n}}$.
To do: To find the value of: $\frac{1}{1+a^{n-m}}+\frac{1}{1+a^{m-n}}$.
Solution:
$\frac{1}{1+a^{m-n}}+\frac{1}{1+a^{n-m}}$
$=\frac{1}{1+\frac{a^m}{a^n}}+\frac{1}{1+\frac{a^n}{a^m}}$
$=\frac{1}{\frac{a^m+a^n}{a^n}}+\frac{1}{\frac{a^m+a^n}{a^m}}$
$=\frac{a^n}{a^m+a^n}+\frac{a^m}{a^m+a^n}$
$=\frac{a^m+a^n}{a^m+a^n}$
$=1$
Thus, $\frac{1}{1+a^{n-m}}+\frac{1}{1+a^{m-n}}=1$.
Updated on: 10-Oct-2022
48 Views
Advertisements