All categories

3 years ago

Make a rational expression out of the polynomial x2 with it as numerator and denominator

Mathematics

1 answer:

frosja888 [35]3 years ago

3 0

Answer

x/2

Step-by-step explanation:

You might be interested in

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

Plllllllllllllllllleassssssssseeeeeeeeee help

Vlad1618 [11]

Answer:

1/(5^12 * 32^3 * 9^15)

Step-by-step explanation:

5^-12 = 1/(5^12)

32^-3 = 1/(32^3)

9^-15 = 1/(9^15)

1/(5^12) * 1/(32^3) * 1/(9^15) = 1/(5^12 * 32^3 * 9^15)

8 0

2 years ago

Please help will give give brainliest.

IRINA_888 [86]

..........................

8 0

3 years ago

Read 2 more answers

a student spent 15 minutes painting a 2 foot by 3 foot bulletin board. to the nearest tenth of a minute, how long did it take th

Katyanochek1 [597]

Area of the board divided by the time

2 x 3 = 6ft^2

15/6= 2.5mins

8 0

2 years ago

I don't understand any of these questions

Xelga [282]

20 because there are many more

6 0

3 years ago

Read 2 more answers