Question

plz give the solution​

Answer 1

(2)n + (2/2)n / (2.2)n - (2)n =

(2)n/(2)n ×{1+(1/2)/( 2-1)} = 3/2

Answer 2

Step-by-step explanation:

$i) \: \: \frac{ {2}^{n} + {2}^{n - 1} }{ {2}^{n + 1} - {2}^{n} } = \frac{ {2}^{n} + \frac{ {2}^{n} }{2} }{( {2}^{n}.2 ) - {2}^{n} } \\ \\ = \frac{ \frac{2.{2}^{n} + {2}^{n} }{2} }{ {2}^{n} } \\ \\ = \frac{ \frac{3 .\cancel{ {2}^{n}} }{2} }{ \cancel{{2}^{n}} } \\ \\ = \frac{3}{2} \\ hence \: it \: is \: proved$

$ii)\:\:\frac{ {6}^{n + 3} - 32. {6}^{n + 1} }{ {6}^{n + 2} - 2. {6}^{n + 1} } = \frac{ {6}^{n} . {6}^{3} - 32 . {6}^{n} .6 }{ {6}^{n}. {6}^{2} - 2. {6}^{n} .6 } \\ \\ = \frac{ \cancel {{6}^{n}}( {6}^{3} - 32 \times 6) }{ \cancel{ {6}^{n} }( {6}^{2} - 2 \times 6)} \\ \\ = \frac{216 - 192}{36 - 12} \\ \\ = \frac{24}{24} \\ \\ = 1 \\ hence \: it \: is \: proved.$