How did this conversion took place ?

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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.
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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
 
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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.
 

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