Question

16*2^n+1 - 4*2^n/16*2^n+2-2*2^n+1
Please solve this equation

Answer 1

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!