How did this conversion took place ?

  • Thread starter Thread starter Sumedh
  • Start date Start date
AI Thread Summary
The discussion centers on the derivation of a summation formula from an initial expression, specifically transitioning from 6(2)^(n-2) + 1 to 6(2)^(n-1) + n + 2. Participants clarify that the two expressions are not equivalent and emphasize that they are expressions rather than equations, lacking an equality sign. A specific example using n = 2 demonstrates that the values produced by both expressions do not match, indicating a misunderstanding in the summation process. There is also a request for clarification on the notation and potential missing symbols. Ultimately, the conversation highlights the need for accurate mathematical representation in problem-solving.
Sumedh
Messages
61
Reaction score
0

Homework Statement


6(2)^(n-2) +1

then summation of above equation will be
6(2)^(n-1) + n + 2

can you please tell me how this equaton came from the first equation?

The Attempt at a Solution



the later formula is correct summation of the former

because it may look that the summation is
6(2)^(n-1) +n - 3

but by putting values of n-
6(2)^(n-1) +n - 3 is incorrect

please help as how the topmost formula gives the second formula
 
Last edited:
Physics news on Phys.org
Sumedh said:

Homework Statement


6(2)^(n-2) +1

then summation of above equation will be
6(2)^(n-1) + n + 2

can you please tell me how this equaton came from the first equation?
It doesn't. First off, these aren't equations - they are expressions. An equation is a statement that two expressions are equal, and always has an = symbol in it.

Starting from your first expression,
6\cdot2n-2 + 1 = 6\cdot2n-1\cdot(1/2) + 1 = 3\cdot2n-1 + 1

To show that your two expressions above aren't identically equal, let n = 2. Then 6\cdot2n-2 + 1 = 6 * 1 + 1 = 7.

And 6\cdot2n-1 + n + 2 = 6* 2 + 2 + 2 = 16.

Sumedh said:

The Attempt at a Solution



the later formula is correct summation of the former

because it may look that the summation is
6(2)^(n-1) +n - 3

but by putting values of n-
6(2)^(n-1) +n - 3 is incorrect

please help as how the topmost formula gives the second formula
 
I'm not sure what these expressions (and these are expressions, not equation) are. Are there any symbols missing? Can you attach an image, or retype using LaTeX?
 
I get a "page is unavailable" error.
 

Thread 'Finding the number of ways to arrange identical balls in a circle (3 different colors)'

I tried to combine those 2 formulas but it didn't work. I tried using another case where there are 2 red balls and 2 blue balls only so when combining the formula I got ##\frac{(4-1)!}{2!2!}=\frac{3}{2}## which does not make sense. Is there any formula to calculate cyclic permutation of identical objects or I have to do it by listing all the possibilities? Thanks
View full post »

Similar threads

Solve Summation Change of Index: Find $\sum_{k=0}^{n} k^2$
Replies
2
Views
2K
Proof by induction (summation)
Replies
6
Views
2K
How to find z^n of a complex number
Replies
12
Views
3K
Proof by Induction: Arithmetic Sum
Replies
9
Views
3K
How do you solve cos(α+θ)=0 for different values of α?
Replies
21
Views
2K
Relation between vector length and direction ratios
Replies
3
Views
2K
Algorithm analysis problem turned into a math problem
Replies
6
Views
2K
Rewrite an even of N series as a function of N
Replies
4
Views
2K
Trigonometric equation of two sines
Replies
8
Views
2K
Math olympiad products question
Replies
33
Views
3K

Hot Threads

Recent Insights

Back
Top