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Ahat [919]
3 years ago
11

. Evaluate the series 1 + 0.1 + 0.01 + . . .

Mathematics
2 answers:
EastWind [94]3 years ago
6 0

We can employ a simple repeated decimal trick:

x=1.111\ldots

0.1x=0.111\ldots

\implies x-0.1x=1\implies0.9x=1\implies x=\dfrac1{0.9}=\dfrac{10}9

###

Alternatively, we can compute the partial sum of the series.

\displaystyle S_n=\sum_{k=0}^n\dfrac1{10^k}

S_n=1+0.1+0.01+\cdots+\dfrac1{10^n}

0.1S_n=0.1+0.01+0.001+\cdots+\dfrac1{10^{n+1}}

\implies S_n-0.1S_n=0.9S_n=1-\dfrac1{10^{n+1}}

\implies S_n=\dfrac{10}9-\dfrac9{10^n}

As n\to\infty, the second term vanishes and we're left with \dfrac{10}9. Notice that this is really just a more formal version of the earlier trick.

amm18123 years ago
5 0

Answer:

1.11

Step-by-step explanation:

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uysha [10]

Hi there!

nearest percentage=64%

<em><u>1.Subtract starting value and final value:</u></em>

<em><u /></em>1599-579=1020<em><u /></em>

<em><u>2.Divide it by the starting value:</u></em>

<em><u /></em>1020*1599= 0.6378986866791744840525328330206378986<em><u /></em>

<em><u>3.Multiply the term by 100:</u></em>

<em><u /></em>0.6378986866791744840525328330206378986<em><u>·</u></em>100= 63.78986866791744840525328330206378986<em><u /></em>

<em><u>4.Round the term:</u></em>

<em><u /></em>63.78986866791744840525328330206378986=64<em><u /></em>

Therefore, the decrease of the total 8 years was 64%.

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5 0
3 years ago
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The cost of a pair of boots at a certain store is 145% of the cost of a pair of sneakers. The pair of sneakers costs $21.
Vilka [71]

Answer:

so $21+45%=30.45. meaning that pair of boots cost 30.45 so two pairs of boots would cost $60.90

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Murrr4er [49]
Well there are 6 units down and 11 units across so 6•11=66. there are 14 red units. 66-14=52. the area of yellow is 52.
4 0
3 years ago
4. Can two lines be parallel and perpendicular? Explain.
lidiya [134]

Answer: No

Step-by-step explanation: First, we need to understand that parallel lines are coplanar lines that do not intersect. On the other hand, perpendicular lines are lines that intersect at a right angle.

However, lines can't be both parallel and perpendicular because they either intersect each other at a right angle or never intersect.

So no, two lines can't be both parallel and perpendicular.

7 0
3 years ago
9/11 = ?/22<br> a. 12<br> b. 9<br> c. 4<br> d. 18
svlad2 [7]
18/22 = 2*9/2*11 = 9/11

Therefore, your answer is 18
7 0
3 years ago
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