How to obtain the sum?

Question

Find the sum of the first seven terms of the sequence.

3, 3/2, 3/4,... 3/8, 3/16, 3/32, 3/64

So i get that the LCM is 64 but how do i find the sum of all the 3's? 

Thanks

Answer 1

Rob, 

 

When adding and subtracting fractions (you can look at the whole number 3 as 3/1) you would need to multple the numerator and the denominator by the value that gives the LCD. 

 

You will get the following: 

 

3 = 192/64

3/2 = 96/64

3/4 = 48/64

3/8 = 24/64

3/16 = 12/64

3/32 = 6/64

3/64 = 3/64

 

Your answer should be: 381/64 or 5 and 61/64

 

Hope this helps!

Answer 2

If you don't want to add all those 3's in the numerator, then there is an alternate way.

 

If you look carefully, you will realize that you get each subsequent term by multiplying the previous term by 1/2

 

Well, that makes it a geometric series with first term, a = 3 and common ratio, r = 1/2

 

So, you can use the formula for the sum of first n terms of a geometric sequence: a(1-rⁿ) / (1-r)

 

Plug in the values: a=3, r=1/2 and n=7

 

sum =3[1-(1/2)⁷] / (1-1/2)

=3[1-1/128] / (1/2)

=6[127/128]

= 381/64