Find the sum of the series 1-3+5-7+-11+ +1001

In summary, the problem is asking for the sum of the series 1-3+5-7+-11+...+1001. After clarifying the sequence, it can be rewritten as 1+ (5-3)+ (9-7)+ (13-11)+ ...+ (1001-999), which simplifies to 1+ 2+ 2+ 2+ ...+ 2. There are 500 odd integers from 3 to 1001, meaning there are 250 pairs of odd numbers. Therefore, the sum of the sequence is 501.
  • #1
rought
34
0

Homework Statement



Find the sum of the series 1-3+5-7+-11+...+1001


Homework Equations



I have no idea on this one...

I do know that the sum formula is Sn=n(t1+tn)/2
 
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  • #2
That formula only applies to arithmetic sequences and this is not an arithmetic sequence.

The first thing you will need to do is clarify the sum: 1-3+5-7+-11+...+1001. the first numbers, in absolute value, 1, 3, 5, and 7 differ by 2 but then there is the jump to 11, 4 larger than 7. Is it supposed to be 1-3+5-7+9-11+...+1001? If so then you can rewrite it 1+ (5-3)+ (9-7)+ (13- 11)+ ...+ (1001-999)= 1+ 2+ 2+ 2+ ...+ 2. Now, how many "2"s are there? How many pairs of odd numbers are there from 5 to 1001?
 
  • #3
HallsofIvy said:
That formula only applies to arithmetic sequences and this is not an arithmetic sequence.

The first thing you will need to do is clarify the sum: 1-3+5-7+-11+...+1001. the first numbers, in absolute value, 1, 3, 5, and 7 differ by 2 but then there is the jump to 11, 4 larger than 7. Is it supposed to be 1-3+5-7+9-11+...+1001? If so then you can rewrite it 1+ (5-3)+ (9-7)+ (13- 11)+ ...+ (1001-999)= 1+ 2+ 2+ 2+ ...+ 2. Now, how many "2"s are there? How many pairs of odd numbers are there from 5 to 1001?


Yes sorry, there is supposed to be a 9 in there...

So there would be 999 "2"s ?

Would there be 200 pairs of odd numbers?
 
  • #4
an=a+(n-1)d
1001=3+(n-1)2
1001-3=(n-1)2
998/2=n-1
499=n-1
499+1=n
n=500

500 odd integers from 3-1001

Therefore,
250 2s

250*2=500
500+1=501

Therefore,
the sum of the sequence=501 :wink:
 

FAQ: Find the sum of the series 1-3+5-7+-11+ +1001

What is the pattern of this series?

The pattern of this series is an alternating sequence of adding and subtracting odd numbers, starting with 1 and ending with 1001.

How many terms are in this series?

There are 501 terms in this series, as it includes every odd number from 1 to 1001.

What is the sum of this series?

The sum of this series is 501, as each term is either added or subtracted from the previous term, resulting in a constant increase of 2. Therefore, the sum can be calculated by dividing the number of terms (501) by 2, resulting in a final sum of 501.

What is the significance of using odd numbers in this series?

The use of odd numbers in this series creates a pattern that can be easily identified and calculated, as the numbers increase by a constant value of 2. This also allows for the sum of the series to be easily calculated by dividing the number of terms by 2.

Can this series be simplified or expressed in a different form?

Yes, this series can be simplified by using mathematical notation, such as sigma notation. It can also be expressed as a mathematical equation, where n represents the number of terms in the series: (-1)^{n+1}(2n-1).

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