I found this question in my math textbook and i don't understand it. find the formula for 1/2,3/4,5/8,7/16

Question

The book states that you use both arithmetic and geometric sequences to solve this. the numerators hav a arithmetic sequence 1,3,5,7.. add 2 AND the denominators have a geometric sequence 2,4,8,16 multiply 2..the book states the formula for arithmetic sequence is a+(n-1)d
and geometric is ar^n-1
the aswer the book gives is 2n-1/2n
i don't get how they got 2n for the demoninator??
2^1*2^n-1=2n shouldn;t this =4n, y is 2()2) not done ???

Answer 1

I believe the correct answer is actually:
(2n - 1) / 2^n

It should be an exponent in the denominator because the denominator is increasing exponentially to powers of 2. That fits better, because the number work out as 2, 4, 8, 16, etc.

Answer 2

Arithmetice Sequence/Geometric Sequence
a + (n - 1) d/ar^(n-1)
In the arithmmetic sequence
a =1 the first term
d = 2 the common difference
In geomtric sequencee
a = 2 the first term
r = 2 the factor difference
So
(1 + (n - 1)2)/(2 x 2^(n-1))
(1 + 2n - 2)/(2 ^(n - 1 + 1))
(2n - 1)/(2^n)
The denominator is 2 to the power 'n' - Have you misread the textbook/misprint.
2^1*2^n-1 should be written for clarity
2^1*2^(n-1)
Then
2^(n-1+1)
2^n

Answer 3

Correct answer is (2n-1)/(2^n)

Answer 4

2n-1/ 2^n
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Answer 5

1/2,3/4,5/8,7/16
(2n-1)/2^n

Answer 6

1/2.3/4,5/8.......


2n-1/2^n

when n=1,2,3,4,5,..........