Posted by **Anonymous** on Sunday, September 18, 2011 at 7:53pm.

Im stuck on a lot of questions, here they are:

24 + 12 + 6 + ...(S7)

Sn = 24(2^7-1)/2-1

S7 = 24(127)/1

S7 = 3048/1

Thats what I got as an answer, but it's wrong, the real answer is a fraction answer, and its 381/8. How did they get that???

The other one was:

512 + (-256) + 128 +... +(-1)

Sn = -2(-1)-512/-2-1

= -510/-3

This answer is somehow wrong too:/

And the other one:

-8 -2 -1/2...-1/128

Sn = 4(-1/128)-8/4-1

Sn = 4/1 * 128/1 = 512 *-8

Sn = -4096/3

= This is also the wrong answer. Im soo confused ://// It's supposed to be 1356/128

- MATH HELP Calculus -
**Reiny**, Sunday, September 18, 2011 at 8:30pm
1st:

your r value is 1/2, you used it as +2

Sum(7) = 24((1/2)^7 - 1)/(1/2-1)

= 24(1/128 - 1)/(-1/2)

= 24(-127/128)(-2) = 381/8

2nd:

a = 512 , r = -1/2

first find number of terms, last term is -1

t(n) = ar^(n-1)

-1 = 512(-1/2)^(n-1)

-1/512 = (-1/2)^(n-1)

(-1/2)^9 = (-1/2)^(n-1)

9 = n-1

n = 10

so Sum(10) = 512((-1/2)^10 - 1)/(-1/2-1)

= 512(-513/512)(-2/3)

= 342

3rd:

-8 - 2 - 1/2 - ... - 1/128

a = -8 , r = 1/4 , n = ??

term(n) = ar^(n-1)

-1/128 = -8(1/4)^(n-1)

1/1024 = (1/4)^n-1

(1/4)^5 = (1/4)^(n-1)

5 = n-1

n = 6

the series is

-8 -2 -1/2 -1/8 -1/32 - 1/128

sum(6) = -8((1/4)^6 - 1)/(1/4 -1)

= -8(-4095/4096)/(-3/4)

= -8(-4095/4096)(-4/3)

= -1365/128

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