- #1
PrudensOptimus
- 641
- 0
How do you find the sum of the digits of number N?
Say N = 10
Say N = 10
How do you find the sum of the digits of number N? Say N = 10
- Context: High School
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Discussion Overview
The discussion revolves around the method for finding the sum of the digits of a number N, with specific examples provided, including N = 10 and a much larger number. Participants explore different interpretations of the question and the implications of summing digits versus summing a series of integers.
Discussion Character
- Exploratory, Debate/contested, Conceptual clarification
Main Points Raised
- One participant asks how to find the sum of the digits of N, specifically using N = 10 as an example.
- Another participant references the formula for the sum of the first N integers, suggesting it might relate to the question but acknowledges it requires proof by induction.
- A participant clarifies that the sum of the digits of 10 is 1 + 0 = 1, indicating a potential misunderstanding of the original question.
- One participant notes that the formula for the sum of integers only holds under certain conditions, such as when the digits form an arithmetic progression, and provides an example with N = 12245.
- Another participant admits to having answered a different question than intended, expressing a light-hearted acknowledgment of the confusion.
- A participant introduces a hypothetical scenario involving a much larger N, prompting further exploration of how to sum the digits in such a case.
- Another participant humorously expands on the previous point, illustrating the sum of digits for a long number with a playful tone.
Areas of Agreement / Disagreement
Participants do not reach a consensus on the interpretation of the original question, with multiple competing views on how to approach the sum of digits versus the sum of a series of integers.
Contextual Notes
Some assumptions about the nature of N and the definitions of summing digits versus summing integers remain unresolved, leading to varied interpretations of the question.
- #2
BigRedDot
- 42
- 2
If memory serves me correctly:
[tex] \sum_{k=1}^N k= \frac{N(N+1)}2[/tex]
a fact that you would prove by induction.
[tex] \sum_{k=1}^N k= \frac{N(N+1)}2[/tex]
a fact that you would prove by induction.
- #3
HallsofIvy
Science Advisor
Homework Helper
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Was that what was meant? The "sum of the digits" of 10 is 1+ 0= 1, of course.
- #4
himanshu121
- 649
- 1
It will be true only if the digits form a Arithmetic Projection
for eg N=2468 etc {2+4+6+8}
but not in general say for N=12245 {1+2+2+4+5}
- #5
BigRedDot
- 42
- 2
You're right, I answered a completely different question. Well, I am sure someone asked my question somewhere, sometime. :)
- #6
PrudensOptimus
- 641
- 0
Yea what if N = 1231247839783924723840723084732084738274... + ... N?
- #7
himanshu121
- 649
- 1
Ofcourse it would be
as N=1+0
here it will be N=1+2+3+1+2+4+7+8+3+9+7+8+3+9+2+4+7+2+3+8+4+0+7+2+3+0+8+4+7+3+2+0+8+4+7+3+8+2+7+4+...+x+y+z+a+b+c+d
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