11+2a−b+11+2b−a11+2a−b+11+2b−a\frac{1}{{1 + {2^{a - b}}}} + \frac{1}{{1 + {2^{b - a}}}} is equal to = ?" /> 11+2a−b+11+2b−a11+2a−b+11+2b−a\frac{1}{{1 + {2^{a - b}}}} + \frac{1}{{1 + {2^{b - a}}}} is equal to = ?" /> 11+2a−b+11+2b−a11+2a−b+11+2b−a\frac{1}{{1 + {2^{a - b}}}} + \frac{1}{{1 + {2^{b - a}}}} is equal to = ?" />

India’s No.1 Educational Platform For UPSC,PSC And All Competitive Exam

Download Our App

$\frac{1}{1 + 2^{a - b}} + \frac{1}{1 + 2^{b - a}}$ $\frac{1}{{1 + {2^{a - b}}}} + \frac{1}{{1 + {2^{b - a}}}}$ is equal to = ?

1a - b
2b - a
31
40

Answer:- 1

Explanation:-

Solution:

\begin{aligned} \frac{1}{1 + 2^{a - b}} + \frac{1}{1 + 2^{b - a}} \\ = \frac{1}{1 + 2^{a - b}} + \frac{1}{1 + 2^{- (a - b)}} \\ = \frac{1}{1 + 2^{a - b}} + \frac{2^{a - b}}{2^{a - b} + 1} \\ = \frac{1 + 2^{a - b}}{1 + 2^{a - b}} \\ = 1 \end{aligned}

Workspace Report

Post your Comments

is equal to = ?", "text": "

\frac{1}{1 + 2^{a - b}} + \frac{1}{1 + 2^{b - a}}

$\frac{1}{{1 + {2^{a - b}}}} + \frac{1}{{1 + {2^{b - a}}}}$ is equal to = ?", "dateCreated": "7/24/2019 10:09:12 AM", "author": { "@type": "Person", "name": "Nitin Sir" }, "answerCount": "4", "acceptedAnswer": { "@type": "Answer", "text": "

Solution:

\begin{aligned} \frac{1}{1 + 2^{a - b}} + \frac{1}{1 + 2^{b - a}} \\ = \frac{1}{1 + 2^{a - b}} + \frac{1}{1 + 2^{- (a - b)}} \\ = \frac{1}{1 + 2^{a - b}} + \frac{2^{a - b}}{2^{a - b} + 1} \\ = \frac{1 + 2^{a - b}}{1 + 2^{a - b}} \\ = 1 \end{aligned}

$\eqalign{ & \frac{1}{{1 + {2^{a - b}}}} + \frac{1}{{1 + {2^{b - a}}}} \cr & = \frac{1}{{1 + {2^{a - b}}}} + \frac{1}{{1 + {2^{ - \left( {a - b} \right)}}}} \cr & = \frac{1}{{1 + {2^{a - b}}}} + \frac{{{2^{a - b}}}}{{{2^{a - b}} + 1}} \cr & = \frac{{1 + {2^{a - b}}}}{{1 + {2^{a - b}}}} \cr & = 1 \cr}$ ", "dateCreated": "7/24/2019 10:09:12 AM", "author": { "@type": "Person", "name": "Nitin Sir" } }, "suggestedAnswer": { "@type": "Answer", "text": "

Solution: