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Sum the series 1.58+1.582+1.583+…+1.5832
- Thread starter khession
- Start date
Sum the series 1.58+1.582+1.583+…+1.5832. Round your answer to the nearest tenth.
I am unsure how to go about solving this problem. Anyone have any ideas?
I don't see a pattern in the sum. It appears as if you skipped some terms. I'm not
stating necessarily that you did skip any, but I don't see consistency in the terms
of your series.
I don't see a pattern in the sum. It appears as if you skipped some terms. I'm not
stating necessarily that you did skip any, but I don't see consistency in the terms
of your series.
Sorry those were meant to be exponents but nope thats alll the problem says!
Sum the series 1.58+1.58^2+1.58^3+…+1.58^32. Round your answer to the nearest tenth.
Last edited by a moderator:
Sorry those were meant to be exponents but nope thats alll the problem says!
Sum the series 1.58+1.58^2+1.58^3+…+1.58^32. Round your answer to the nearest tenth.
khession, no, the above doesn't make sense either. If the instructions are to round your answer
to the nearest tenth, then it would make sense for the problem to be this:
\(\displaystyle 1.58 \ + \ 1.58^2 \ + \ 1.58^3 \ + \ ... \ + \ 1.58^{32} \ \ \ \ \ \ \ \ \ \ \ \ \) (Notice how you had decimals in your first post.)
Please check the problem again. Rounding to the nearest tenth doesn't make sense if
only integers are being summed.
Moderator Note: fixed all decimal points; my bad.
Last edited by a moderator:
HallsofIvy
Elite Member
- Joined
- Jan 27, 2012
- Messages
- 7,763
For any number, a, 1+ a+ a^2+ a^3+ ...+ a^N is a "geometric sum" and can be done like this:
Let S= 1+ a+ a^2+ a^3+ ...+ a^N. Then S= 1+ a(1+ a+ ...+ a^(N- 1))
S= 1+ a(1+ a+ ...+ a^(N- 1)+ a^N- a^N)= 1+ a(S- a^N)= 1+ aS- a^(N+1)
S- aS= 1- a^(N+ 1)
(1- a)S= 1- a^(N+1)
S= (1- a^(N+ 1))/(1- a).
Here, a= 1.58, N= 32, and there is no "1" at the start.
If there were a "1" at the start, the sum would be (1- 1.58^32)/(1-1.58).
To account for the missing "1", subtract 1: (1- 1.58^32)/(-.58)- 1.
Let S= 1+ a+ a^2+ a^3+ ...+ a^N. Then S= 1+ a(1+ a+ ...+ a^(N- 1))
S= 1+ a(1+ a+ ...+ a^(N- 1)+ a^N- a^N)= 1+ a(S- a^N)= 1+ aS- a^(N+1)
S- aS= 1- a^(N+ 1)
(1- a)S= 1- a^(N+1)
S= (1- a^(N+ 1))/(1- a).
Here, a= 1.58, N= 32, and there is no "1" at the start.
If there were a "1" at the start, the sum would be (1- 1.58^32)/(1-1.58).
To account for the missing "1", subtract 1: (1- 1.58^32)/(-.58)- 1.