MHB Summation and product notation rules

Click For Summary
The discussion focuses on the validity of statements regarding summation and product notation rules. The user initially believes that only two statements are correct and identifies the third statement as incorrect, specifically regarding the distribution of a constant across a product. The conclusion confirms that the user's assessment is accurate, affirming that the third statement does not hold true. The conversation emphasizes the importance of understanding the properties of summation and product notation in mathematical expressions. Overall, the user successfully clarifies their understanding of the rules.
lemonthree
Messages
47
Reaction score
0
As per the image, I am supposed to select all the valid statements. Apparently I'm only partially correct, and so I took another look at the statements.

I believe the third statement is wrong, since $$c * (a_m*a_{m+1}*a_{m+2}*...*a_n)$$ =/= $$ (c*a_m)(c*a_{m+1})(c*a_{m+2})*...*(c*a_n)$$

Thus there should only be two answers. Am I correct on this?
 

Attachments

  • Capture.JPG
    Capture.JPG
    23.1 KB · Views: 130
Physics news on Phys.org
You are correct.

-Dan
 

Thread 'Two interesting number theory tricks'

First trick I learned this one a long time ago and have used it to entertain and amuse young kids. Ask your friend to write down a three-digit number without showing it to you. Then ask him or her to rearrange the digits to form a new three-digit number. After that, write whichever is the larger number above the other number, and then subtract the smaller from the larger, making sure that you don't see any of the numbers. Then ask the young "victim" to tell you any two of the digits of the...
View full post »

Similar threads

Undergrad A Sequence T based on the Rule of Three
  • · Replies 15 ·
Replies
15
Views
2K
MHB Probability to get a chocolate snowman or a chocolate reindeer
  • · Replies 2 ·
Replies
2
Views
2K
Undergrad Missing(?) rigor in proof involving countable union of countable sets
  • · Replies 10 ·
Replies
10
Views
2K
MHB Upper Bound of Sets and Sequences: Analyzing Logic
  • · Replies 3 ·
Replies
3
Views
5K
Undergrad ##(a_n) ## has +10,-10 as partial limits. Then 0 is also a partial limit
  • · Replies 13 ·
Replies
13
Views
2K
High School Continuation of sequence of supremums question
  • · Replies 9 ·
Replies
9
Views
1K
Undergrad ##(A/\mathfrak{a})_{\mathfrak{p}/\mathfrak{a}}## and its isomorphism?
  • · Replies 31 ·
2
Replies
31
Views
2K
Showing that a state is unentangled under a certain condition
  • · Replies 10 ·
Replies
10
Views
2K
RCL series circuit analysis: Damping Constant
  • · Replies 1 ·
Replies
1
Views
782
MHB Indexed Families of Sets .... Just and Weese .... Exercise 8 ....
  • · Replies 1 ·
Replies
1
Views
2K