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3 years ago

8, 17, 26 find the 31th term

Mathematics

1 answer:

Romashka [77]3 years ago

3 0

Answer:

287

Step-by-step explanation:

each time the number increases by 9

8 + 9 = 17

17 + 9 = 26

26 + 9 = 35

therefore if you continue this pattern you will eventually get 287

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Simplify the expression: 7(–3 + r) =

lina2011 [118]

Answer:

-21+7r

Step-by-step explanation:

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3 years ago

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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

Graph y=1000(1+0.06)^x I don’t have a graphing calculator please help!

a_sh-v [17]

Y=1000(1+00.6) so divide y by 92 and get 1

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3 years ago

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In a building there are 14 pillars. The radius of each pillar is 21 cm and height 3.5 m. Find the cost

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Answer:

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3 years ago

For this item, any answers that are not whole numbers should be entered as decimals, rounded to the hundredth. Marissa's Fashion

trasher [3.6K]

You know that ...

... total cost = (marked-up price) + 6.25% × (marked-up price)

... $90.10 = (marked-up price) × 1.0625

Solving for (marked-up price) gives

... marked-up price = $90.10/1.0625 = $84.80

Markup

You also know that

... marked-up price = cost + markup

... $84.80 = $50.88 + markup

... $33.92 = markup . . . . . . . . . . . subtract $50.88

The percentage of markup can be figured a couple of different ways. It is easy to add a percentage to the cost price of an article, because the cost is generally right in front of the storekeeper when the article is received and prices are being marked. However, many accountants are interested in the percentage of the selling price that is available for overhead and profit, so they are interested in the markup as a percentage of selling price. The question here is non-specific as to the base to be used for figuring the percentage of markup.

The markup as a percentage of cost is

... $33.92/$50.88 × 100% = 66.67%

The markup as a percentage of selling price is

... $33.92/$84.80 × 100% = 40%

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3 years ago

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