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3 years ago

How do I do this, I really need help to understand

Mathematics

1 answer:

Serggg [28]3 years ago

3 0

Which questions do you need help with?

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julia-pushkina [17]

Answer:

Step-by-step explanation:

i just took it

5 0

2 years ago

Read 2 more answers

For the following telescoping series, find a formula for the nth term of the sequence of partial sums

gtnhenbr [62]

I'm guessing the sum is supposed to be

$\displaystyle\sum_{k=1}^\infty\frac{10}{(5k-1)(5k+4)}$

Split the summand into partial fractions:

$\dfrac1{(5k-1)(5k+4)}=\dfrac a{5k-1}+\dfrac b{5k+4}$

$1=a(5k+4)+b(5k-1)$

If $k=-\frac45$ , then

$1=b(-4-1)\implies b=-\frac15$

If $k=\frac15$ , then

$1=a(1+4)\implies a=\frac15$

This means

$\dfrac{10}{(5k-1)(5k+4)}=\dfrac2{5k-1}-\dfrac2{5k+4}$

Consider the $n$ th partial sum of the series:

$S_n=2\left(\dfrac14-\dfrac19\right)+2\left(\dfrac19-\dfrac1{14}\right)+2\left(\dfrac1{14}-\dfrac1{19}\right)+\cdots+2\left(\dfrac1{5n-1}-\dfrac1{5n+4}\right)$

The sum telescopes so that

$S_n=\dfrac2{14}-\dfrac2{5n+4}$

and as $n\to\infty$ , the second term vanishes and leaves us with

$\displaystyle\sum_{k=1}^\infty\frac{10}{(5k-1)(5k+4)}=\lim_{n\to\infty}S_n=\frac17$

7 0

3 years ago

Ahmad,Barry,andTara collected some seashells.Ahmad collected 1 over 6 of the seashells,Barry collected 1and 2 of thr seashell, a

VashaNatasha [74]

Ahmad = 1/6
Barry = 1/2
Tara = 1 - 1/6 - 1/2 = 1/3

1/3 of the seashells = 76
3/3 of the seashells = 76 x 3
3/3 of the seashells = 228

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Answer: They had 228 seashells altogether.
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4 0

3 years ago

In a survey of 400 seniors, x percent said that they plan on majoring in physics. One university has used this data to estimate

azamat

Answer:

2 percent

Step-by-step explanation:

We can use two separate fractions, one representing the amount of physics majors expected and the amount of seniors expected in physics majors by the university.

$\frac{400x}{66} = \frac{400}{3600}$