Find the inequality represented by the graph. dots on (0,5) and (-2,0)

C=1/21.22.23+1/22.23.24+................+1/200.201.202 . = là dấu nhân

Aneli [31]

It looks like you have to find the value of the sum,

$C = \displaystyle \frac1{21\times22\times23} + \frac1{22\times23\times24} + \cdots + \frac1{200\times201\times202}$

so that the n-th term in the sum is

$\dfrac1{(21+(n-1))\times(21+n)\times(21+(n+1))} = \dfrac1{(n+20)(n+21)(n+22)}$

for 1 ≤ n ≤ 180.

We can then write the sum as

$\displaystyle C = \sum_{n=1}^{180} \frac1{(n+20)(n+21)(n+22)}$

Break up the summand into partial fractions:

$\dfrac1{(n+20)(n+21)(n+22)} = \dfrac a{n+20} + \dfrac b{n+21} + \dfrac c{n+22}$

Combine the fractions into one with a common denominator and set the numerators equal to one another:

$1 = a(n+21)(n+22) + b(n+20)(n+22) + c(n+20)(n+21)$

Expand the right side and collect terms with the same power of n :

$1 = a(n^2+43n+462)+b(n^2+42n+440) + c(n^2+41n + 420) \\\\ 1 = (a+b+c)n^2 + (43a+42b+41c)n + 462a+440b+420c$

Then

a + b + c = 0

43a + 42b + 41c = 0

462a + 440b + 420c = 1

==> a = 1/2, b = -1, c = 1/2

Now our sum is

$\displaystyle C = \sum_{n=1}^{180} \left(\frac1{2(n+20)}-\frac1{n+21}+\frac1{2(n+22)}\right)$

which is a telescoping sum. If we write out the first and last few terms, we have

C = 1/(2×21) - 1/22 + 1/(2×23)

… … + 1/(2×22) - 1/23 + 1/(2×24)

… … + 1/(2×23) - 1/24 + 1/(2×25)

… … + 1/(2×24) - 1/25 + 1/(2×26)

… … + … - … + …

… … + 1/(2×198) - 1/199 + 1/(2×200)

… … + 1/(2×199) - 1/200 + 1/(2×201)

… … + 1/(2×200) - 1/201 + 1/(2×202)

Notice the diagonal pattern of underlined and bolded terms that add up to zero (e.g. 1/(2×23) - 1/23 + 1/(2×23) = 1/23 - 1/23 = 0). So, like a telescope, the sum collapses down to a simple sum of just six terms,

C = 1/(2×21) - 1/22 + 1/(2×22) + 1/(2×201) - 1/201 + 1/(2×202)

which we simplify further to

C = 1/42 - 1/44 - 1/402 + 1/404

C = 1,115/1,042,118 ≈ 0.00106994

4 0

3 years ago

Based on the figure below, what is the equation for the relationship of x equals the number of rectangles and y equals the perim

Ad libitum [116K]

Answer:

Are you still there? Continue answering or we'll let someone else answer in: 19:35

Step-by-step explanation:

4 0

3 years ago

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Please help me answer. Thanks in advance.

Aleksandr [31]

72kg - 54kg
180kg - xkg

cross multiply

72 · x = 180 · 54

72x = 9720 |divide both sides by 72

x = 135

Answer: 135kg.

8 0

3 years ago

PLEASE SOLVE DUE RIGHT NOW!!!!!!!!!!!!

erma4kov [3.2K]

Solution:

We know that:

$Area \ of \ triangle = \dfrac{1}{2} \times Base \times Height$

Since we are already given the base and the height, we can substitute them into the formula to find the area of the triangle.

$Area \ of \ triangle = \dfrac{1}{2} \times 18 \times24$

Cancel out the "2" by dividing it by 18.

$Area \ of \ triangle = 9 \times24$

Simplify the multiplication.

$\bold{Area \ of \ triangle = 216 \ ft^{2}}$

6 0

3 years ago

write an eqation for the line that is parrellel to the given line that passes through the given piont y=5/2x-10;(-6,-9)

HACTEHA [7]

Answer:

the red dot is the given point.

Step-by-step explanation:

8 0

3 years ago

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