Precalculus - Page 669 - Possible Mistake

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Precalculus - Page 669 - Possible Mistake

Faraz Rashid
On page 669 of the Precalculus textbook, I think there is a slight mistake in the equality at the top of the page.

The middle and right side of the equalities have "n+1" as the exponent of 10.
I think BOTH these exponents should be "n" instead.

Sum[k=1 to n] 9/10^k = 1 - 1/10^n should be the correct expression.

Equation 9.2 (page 666) is correct, but I think a slight mistake has been made in applying it on page 669, by mixing which of the two expressions in 9.2 we are using.

As an example, we know that
Sum[k=1 to 2] 9/10^k = 9/10 + 9/100 = 0.9 + 0.09 = 0.99

If we use the existing expression on page 669, we get
Sum[k=1 to 2] 9/10^k = 1 - 1/10^(n+1) = 1 - 1/10^(2+1) = 1 - /10^3 = 0.999 which is incorrect.

On the other hand,
Sum[k=1 to 2] 9/10^k = 1 - 1/10^n = 1 - 1/10^2 = 1 - 1/100 = 0.99 is correct.

I think the "n+1" in the equation at the top of page 669 as well as in the short paragraph following the equation should be changed to "n"

Thank you.
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Page 678 - Possible Mistake

Faraz Rashid
Also, on page 678.
Question 8, Part b)
The left hand side of the equations have incorrect letters.

Sum [j=1 to n] ar^{n-1}  SHOULD BE CORRECTED TO
Sum [j=1 to n] ar^{j-1}
for the left side of BOTH r != 1 and r = 1 equations.
The right side of both the equations use the letter "n" correctly.
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Re: Page 678 - Possible Mistake

Carl Stitz
Administrator
Correct on both counts!

Thank you for your careful reading of the text!

Carl
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