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4 years ago

Determine whether the geometric series 25 − 5 + 1 − 0.2 ... converges or diverges, and identify the sum if it exists.

Mathematics

1 answer:

Arturiano [62]4 years ago

5 0

Answer:

Converges

Sum = 20.8333

Step-by-step explanation:

A geometric series has a general formula of:

$\sum ar^n$

Where 'a' is the initial term, 'n' is the number of terms, and 'r' is the constant ratio. If |r| < 1 than the series converges.

In this particular case, the initial term is a=25, and each term is being divided by -5, or multiplied by -0.2, so the general form would be:

$\sum 25*(-0.2)^n$

Since 0.2 < 1.0, the series converges.

The sum of the series is given by:

$S=\frac{a}{1-r}\\S=\frac{25}{1-(-0.2)}\\S=20.8333$

The sum is 20.8333.

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Read 2 more answers

John took all his money from his savings account. He spent $88 on a radio and 1/4 of what was left on presents for his friends.

gayaneshka [121]

Answer:

$968

Step-by-step explanation:

x= the money John originally had in his savings account

The statement says that John spent $88 on a radio and 1/4 of what was left on presents for his friends. This means that the remaining money is 3/4 of the total amount minus the money spent on the radio:

3/4(x-88)

Then, it says that of the money remaining, John put 4/11 into a checking account and the last remaining $420 was left to charity. Since, he spent 4/11 of the remining 3/4(x-88), the remaining is 7/11 of that and that remaining is equal to $420 that was the money left at the end:

7/11(3/4(x-88))= 420

21/44(x-88)=420

21/44x-42=420

21/44x=462

x=968

According to this, the money that John originally had in his savings account was $968.

He spent $88 on a radio: 968-88= 880

1/4 of what was left on presents for his friends: 880/4= 220

880-220=660

Of the money remaining, John put 4/11 into a checking account: 660*(4/11)=240

the last remaining $420 was left to charity: 660-240= 420

6 0

3 years ago

Help plssssssssssssss

SIZIF [17.4K]

The answer is 140

140 x 0.1 (10% as a decimal) = 14

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3 years ago

PLEASE help with these questions??<br> there are 7 of them!<br> Thank you!!

svetlana [45]

We know in these kind of triangles that have a 90 degrees angle, we can do:

${a}^{2} + {b}^{2} = {c}^{2}$

so the first question:

$\sqrt{ {99}^{2} + {20}^{2} } = 101$

and then:

$b = \sqrt{ {17}^{2} - {15}^{2} } = 8$

so , when you want to rationalize , usually you must multiply the irrational factor as 1:

$\frac{ \sqrt{15} }{ \sqrt{15} } = 1$

so , now multiply:

$\frac{3}{ \sqrt{15} } \times \frac{ \sqrt{15} }{ \sqrt{15} } = \frac{3 \sqrt{15} }{15} = \frac{ \sqrt{15} }{5}$

in the next question,we know negative numbers in radical don't have any solution so 2 is correct,

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3 years ago