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Ahat [919]
2 years ago
11

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

Mathematics
2 answers:
EastWind [94]2 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.

amm18122 years ago
5 0

Answer:

1.11

Step-by-step explanation:

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Two friends are collecting stuffed animals. Veronica has 5 more than double the number of stutted
STatiana [176]

v + m = 32 and v = 5 + 2m are the equations that are used  to determine m, the number of stuffed animals Mariposa has

Number of stuffed animals Mariposa has is 9 and number of stuffed animals with Veronica is 23

<h3><u>Solution:</u></h3>

Let "v" be the number of stuffed animals with Veronica

Let "m" be the number of stuffed animals with Mariposa

Given that,

Together, they have 32 stuffed animals

Therefore,

v + m = 32  --------- eqn 1

Veronica has 5 more than double the number of stutted  animals as her friend Mariposa

Therefore,

Number of stuffed animals with Veronica = 5 + 2(number of stuffed animals with Mariposa)

v = 5 + 2m ---------- eqn 2

Thus eqn 1 and eqn 2 can be used to determine m, the number of stuffed animals Mariposa has

Let us solve eqn 1 and eqn 2

Substitute eqn 2 in eqn 1

5 + 2m + m = 32

5 + 3m = 32

3m = 32 - 5

3m = 27

<h3>m = 9</h3>

Substitute m = 9 in eqn 2

v = 5 + 2(9)

v = 5 + 18

<h3>v = 23</h3>

Thus number of stuffed animals Mariposa has is 9 and number of stuffed animals with Veronica is 23

5 0
3 years ago
Anyone knows this?!? ​
IRINA_888 [86]

Answer:

(0.84, 0.88)

Step-by-step explanation:

if you round 0.875 you get 0.88

8 0
2 years ago
What is 1.3742 rounded to the nearest tenth?
REY [17]

Answer:

1.4 that is the true answer

Step-by-step explanation:

go to the place right after the decimal and then look at the number next to it.if it is greater the 5 it goes up to 1.4 and it is

6 0
2 years ago
Nathan needs to sell at least 75 t shirts to get a bonus he already has sold 15 red tye dye shirts and 23 solid blue ones how ma
AnnyKZ [126]

Red shirts and blue shirts equally count to his bonus, so he has 15 + 23 = 38 shirts sold at this moment. He needs to sell 75 shirts for the bonus. We subtract our goal from what he have; 75 - 38 = 37.


The strategy here: subtract the goal (75 shirts) from what you did to get to the goal (15 shirts and 23 shirts).


Nathan needs to sell 37 more shirts for the bonus. Hope this helps.

4 0
3 years ago
Read 2 more answers
6) If 1 Inch = 2.54cm, then set up and solve a proportion that finds how many
Roman55 [17]

Answer:

3.93700787402, almost  4

Step-by-step explanation:

10 ÷ 2.54

3 × 2.50 = 7.50

3 × 0.04 = 0.12

7.50 + 0.12 = 7.65

7.65 + 2.54 = 10.19

The precise number is use calculator.

7 0
2 years ago
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