MATH HELP Calculus
posted by Anonymous on .
Im stuck on a lot of questions, here they are:
24 + 12 + 6 + ...(S7)
Sn = 24(2^71)/21
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)512/21
= 510/3
This answer is somehow wrong too:/
And the other one:
8 2 1/2...1/128
Sn = 4(1/128)8/41
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

1st:
your r value is 1/2, you used it as +2
Sum(7) = 24((1/2)^7  1)/(1/21)
= 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^(n1)
1 = 512(1/2)^(n1)
1/512 = (1/2)^(n1)
(1/2)^9 = (1/2)^(n1)
9 = n1
n = 10
so Sum(10) = 512((1/2)^10  1)/(1/21)
= 512(513/512)(2/3)
= 342
3rd:
8  2  1/2  ...  1/128
a = 8 , r = 1/4 , n = ??
term(n) = ar^(n1)
1/128 = 8(1/4)^(n1)
1/1024 = (1/4)^n1
(1/4)^5 = (1/4)^(n1)
5 = n1
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