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4 years ago

The variables A,B,and C represent polynomials where A=x2, B=3x, and C=x-3 what is AB-C^2 in its simplest form

Mathematics

1 answer:

DedPeter [7]4 years ago

5 0

This is the correct answer: 3x^3 - x^2 + 6x - 9

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For the following telescoping series, find a formula for the nth term of the sequence of partial sums {Sn}. Then evaluate limn→[

Ivenika [448]

Answer:

The following are the solution to the given points:

Step-by-step explanation:

Given value:

$1) \sum ^{\infty}_{k = 1} \frac{1}{k+1} - \frac{1}{k+2}\\\\2) \sum ^{\infty}_{k = 1} \frac{1}{(k+6)(k+7)}$

Solve point 1 that is $\sum ^{\infty}_{k = 1} \frac{1}{k+1} - \frac{1}{k+2}\\\\$ :

when,

$k= 1 \to s_1 = \frac{1}{1+1} - \frac{1}{1+2}\\\\$

$= \frac{1}{2} - \frac{1}{3}\\\\$

$k= 2 \to s_2 = \frac{1}{2+1} - \frac{1}{2+2}\\\\$

$= \frac{1}{3} - \frac{1}{4}\\\\$

$k= 3 \to s_3 = \frac{1}{3+1} - \frac{1}{3+2}\\\\$

$= \frac{1}{4} - \frac{1}{5}\\\\$

$k= n^ \to s_n = \frac{1}{n+1} - \frac{1}{n+2}\\\\$

Calculate the sum $(S=s_1+s_2+s_3+......+s_n)$

$S=\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+.....\frac{1}{n+1}-\frac{1}{n+2}\\\\$

$=\frac{1}{2}-\frac{1}{5}+\frac{1}{n+1}-\frac{1}{n+2}\\\\$

When $s_n \ \ dt_{n \to 0}$

$=\frac{1}{2}-\frac{1}{5}+\frac{1}{0+1}-\frac{1}{0+2}\\\\=\frac{1}{2}-\frac{1}{5}+\frac{1}{1}-\frac{1}{2}\\\\= 1 -\frac{1}{5}\\\\= \frac{5-1}{5}\\\\= \frac{4}{5}\\\\$

$\boxed{\text{In point 1:} \sum ^{\infty}_{k = 1} \frac{1}{k+1} - \frac{1}{k+2} =\frac{4}{5}}$

In point 2: $\sum ^{\infty}_{k = 1} \frac{1}{(k+6)(k+7)}$

when,

$k= 1 \to s_1 = \frac{1}{(1+6)(1+7)}\\\\$

$= \frac{1}{7 \times 8}\\\\= \frac{1}{56}$

$k= 2 \to s_1 = \frac{1}{(2+6)(2+7)}\\\\$

$= \frac{1}{8 \times 9}\\\\= \frac{1}{72}$

$k= 3 \to s_1 = \frac{1}{(3+6)(3+7)}\\\\$

$= \frac{1}{9 \times 10} \\\\ = \frac{1}{90}\\\\$

$k= n^ \to s_n = \frac{1}{(n+6)(n+7)}\\\\$

calculate the sum: $S= s_1+s_2+s_3+s_n\\$

$S= \frac{1}{56}+\frac{1}{72}+\frac{1}{90}....+\frac{1}{(n+6)(n+7)}\\\\$

when $s_n \ \ dt_{n \to 0}$

$S= \frac{1}{56}+\frac{1}{72}+\frac{1}{90}....+\frac{1}{(0+6)(0+7)}\\\\= \frac{1}{56}+\frac{1}{72}+\frac{1}{90}....+\frac{1}{6 \times 7}\\\\= \frac{1}{56}+\frac{1}{72}+\frac{1}{90}+\frac{1}{42}\\\\=\frac{45+35+28+60}{2520}\\\\=\frac{168}{2520}\\\\=0.066$

$\boxed{\text{In point 2:} \sum ^{\infty}_{k = 1} \frac{1}{(n+6)(n+7)} = 0.066}$

8 0

3 years ago

A bicycle rental company charges $10 for a bicycle rental, plus an additional $2.25 per hour that the bicycle is rented. The tot

kondaur [170]

Answer:

7 hours

Step-by-step explanation:

25.75(total cost of the rental)

-10.00 (cost of initially renting the bike)

----------------

15.75$ (cost of hourly fees)

15.75/2.25(hourly rate) = 7

4 0

3 years ago

What is 51 divided by 25

Vesnalui [34]

2 1/25 is the answer

4 0

4 years ago

Read 2 more answers

Starting with the definition 1.00in. = 2.54 cm, find the number of kilometers in 7.00mi . Please describe conversions.

ella [17]

The answer is 11.265408 km.

To calculate the number of kilometers, we will use several conversions:
A) 1 mi = 63,360 in
B) 1 in = 2.54 cm
C) 1 cm = 0.00001 km

A) 1 mi = 63,360 in
7 mi = 63,360 in · 7 = 443,520 in

B) 1 in = 2.54 cm
443,520 in = 2.54 cm · 443,520 = 1,126,540.80 cm

C) 1 cm = 0.001 km
1,126,540.80 cm = 0.00001 km · 1,126,540.80 = 11.265408 km

6 0

3 years ago

Read 2 more answers

Happy paws charges $19.00 plus $1.50 per hour to keep a dog during the day. Woof watchers charges $13.00 plus $2.75 per hour. Co

natta225 [31]

For paws charges $20.50 and woof watchers charge $15.75

6 0

4 years ago