Question

16×2^n+1 - 4×2^n/16×2^n+2 -2×2^n+2

Answer 1

Hello!

$\dfrac{(16 \sf \:x\: 2^{n} \sf \:x\: 2) - (4 \sf \:x\: 2^{n})}{(16 \sf \:x\: 2^{n+2}) - 2 \sf \:x\: 2^{n+2})}$

⇒ $\dfrac{(16 \sf \:x\: 2^{n} \sf \:x\: 2) - (4 \sf \:x\: 2^{n})}{(16 \sf \:x\: 2^{n} \sf \:x\:2^{2}) - (2 \sf \:x\: 2^{n} \sf \:x\:2^{2})}$

⇒ $\dfrac{\cancel{4 \sf \:x\: 2^{n}}(4 \sf \:x\:2 - 1)}{\cancel{4 \sf \:x\: 2^{n}}(16-2)}$

⇒ $\dfrac{8-1}{16-2}$ ⇒ $\dfrac{7}{14} = \boxed{\blue{\bf{\dfrac{1}{2}}}}$

Cheers!

Answer 2

Answer:

Hello Mate!

Question = [ 16 × 2^( n + 1 ) - 4 × 2^n ]/[ 16 × 2^( n + 2 ) - 2 × 2^( n + 2 ) ]

Numerator

= 16 × 2^( n + 1 ) - 4 × 2^n

= 16 × 2^n × 2¹ - 4 × 2^n

= 2^n( 16 × 2 - 4 )

= 2^n( 32 - 4 )

= 2^n( 28 )

Denominator

= 16 × 2^( n + 2 ) - 2 × 2^( n + 2 )

= 16 × 2^n × 2² - 2 × 2^n × 2²

= 2^n( 16 × 4 - 2 × 4 )

= 2^n( 64 - 8 )

= 2^n( 56 )

Now, fraction = 2^n( 28 ) / 2^n( 56 )

= 1 / 2

Hence answer is ½.

Have great future ahead!