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2 years ago

Two positive, consecutive, odd integers have a product of 143. set up an equation to then solve for the integers.

Mathematics

1 answer:

mixer [17]2 years ago

6 0

Answer:

Step-by-step explanation:

Let (2n-1) and (2n+1) be the consecutive, odd numbers.

(2n-1)(2n+1) = 143

4n² - 1 = 143

4n² = 144

n² = 36

n = 6

2n-1 = 11

2n+1 = 13

The numbers are 11 and 13.

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Is My answer correct?

Licemer1 [7]

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3 years ago

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anyanavicka [17]

Answer:

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Step-by-step explanation:

The sum you are trying to understand is this.

$\sum\limits_{n=0}^{\infty} \frac{2}{3^n}\frac{(-1)^n}{5^n}$

Remember that in general when you have a geometric series

$\sum\limits_{n = 0}^{\infty} a*r^n$ you have that

$\sum\limits_{n = 0}^{\infty} a*r^n = \frac{a}{1-r}$ and that equality is true as long as $|r| < 1$ .

Therefore here we have

$\sum\limits_{n=0}^{\infty} \frac{2}{3^n}\frac{(-1)^n}{5^n} = \sum\limits_{n=0}^{\infty} 2* \big(\frac{-1}{3*5} \big)^n = \sum\limits_{n=0}^{\infty} 2* \big(\frac{-1}{15} \big)^n$ and $\big|\frac{-1}{15} \big| = \frac{1}{15} < 1$

Therefore we can use the formula and

$\sum\limits_{n=0}^{\infty} 2* \big(\frac{-1}{15} \big)^n = \frac{2}{1-(-1/15)} = \frac{2}{1+1/15} = 30/16 = 15/8$

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Step-by-step explanation:

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kolezko [41]

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