How many terms are in this series?

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Homework Help Overview

The discussion revolves around determining the number of terms in a series expressed in sigma notation, specifically involving the expression \(\sum_{i=7}^{92}(-7)^{i+7}\). Participants are exploring the implications of the notation and the calculations involved in counting the terms.

Discussion Character

  • Exploratory, Assumption checking, Problem interpretation

Approaches and Questions Raised

  • Participants are attempting to clarify the notation and the limits of the summation. Questions arise regarding the interpretation of the index "i" and whether it represents a natural number. Some participants suggest different methods for counting the terms, while others express confusion about the setup.

Discussion Status

The discussion is active, with various interpretations being explored. Some participants have proposed calculations for the number of terms, while others are questioning the clarity of the original expression. There is no explicit consensus on the correct number of terms, but guidance has been offered regarding the counting method.

Contextual Notes

Participants are working with the assumption that the series starts at \(i=7\) and ends at \(i=92\). There is some confusion regarding the exponent in the series and the implications of the limits of summation.

aisha
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I have a question is sigma notation

92
E (-7)^i+7
i=7

Is the number of terms in this series 99? Or

86, 89, or 96 I am so confused PLZ HELP IMMEDIATELY

I think it is 99 because 92+7=99 but I am not sure
 
Last edited:
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Please write it more clearly.Is that "i" [itex]\sqrt{-1}[/itex]...?

Use LaTex.

Daniel.
 
no its

(-7) to the exponent (i+7)

hurry help
 
So that "i" wanders through "n"...?

Daniel.

P.S.If so,then is 99 a natural power of 7...?
 
Is this your sum?

[tex]\sum_{i=7}^{92}(-7)^{i-7}[/tex]

You have a term for each number 7, 8, 9, ..., 91, 92. How many numbers on this list?
 
OMG,i didn't understand the question...No wonder the ballooney...:eek:

So it was that simple...

Daniel.
 
I believe there are 86 in the terms. you take 92-7+1=86
 
Looks like a simple geometric sum to me.
[tex]\sum_{i=7}^{92}(-7)^{i-7}[/tex]

Let n= i- 7 so that when i= 7, n=0 and when i= 92, n= 92-7= 85 (as Gieuseppe said).

The sum is the same as [tex]\sum_{n=0}^{85}(-7)^{n}[/tex].

Can you do that? (There is a simple formula for geometric sums.)
 
[tex]\sum_{i=7}^{92}(-7)^{i+7}[/tex]

the exponent is i plus 7 not minus. Also the answer is 86 not 85 but I don't know how to get the answer I tried so many times.
 
  • #10
Can you answer the question how many numbers are on the list 7, 8, 9, ..., 92?

How about we subtract 6 from each number. The list:

7, 8, 9, ..., 92

has the same number of items as:

1, 2, 3, ..., 86



In general if you have a sum whose index ranges from a to b, you have b-a+1 terms.
 

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