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3 years ago

State why the series is convergent or divergent, and if it is convergent, find the sum.

Mathematics

1 answer:

MatroZZZ [7]3 years ago

8 0

Answer:

Converges, 10

Step-by-step explanation:

∑ 5 / 2ⁿ⁻¹

= ∑ 5 (½)ⁿ⁻¹

This is a geometric series with a₁ = 5 and r = ½. Since |r| < 1, the series converges to:

S = a₁ / (1 − r)

S = 5 / (1 − ½)

S = 10

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What is the sum of the first 37 terms of the arithmetic sequence?

lidiya [134]

Answer:

The sum of the first 37 terms of the arithmetic sequence is 2997.

Step-by-step explanation:

Arithmetic sequence concepts:

The general rule of an arithmetic sequence is the following:

$a_{n+1} = a_{n} + d$

In which d is the common diference between each term.

We can expand the general equation to find the nth term from the first, by the following equation:

$a_{n} = a_{1} + (n-1)*d$

The sum of the first n terms of an arithmetic sequence is given by:

$S_{n} = \frac{n(a_{1} + a_{n})}{2}$

In this question:

$a_{1} = -27, d = -21 - (-27) = -15 - (-21) = ... = 6$

We want the sum of the first 37 terms, so we have to find $a_{37}$

$a_{n} = a_{1} + (n-1)*d$

$a_{37} = a_{1} + (36)*d$

$a_{37} = -27 + 36*6$

$a_{37} = 189$

Then

$S_{37} = \frac{37(-27 + 189)}{2} = 2997$

The sum of the first 37 terms of the arithmetic sequence is 2997.

6 0

3 years ago

The pie chart shows information about voters in an election. 3360

Lesechka [4]

Answer:

4838 total number of voters

Step-by-step explanation:

In a whole circle there 360°, in a straight line theres 180°.

180-110=70 first to break it down to find the degrees of women.

180+70=250° for women.

250°=3360

we need to find 110° of men

25°=336

times 4

100°=1344

divide by 10

10°=134.4 round down 134

1344+134=1478

3360+1478=4838

7 0

3 years ago

In Triangle WVU, what sides include Angle V?

NeTakaya

Answer:

∴ $WV$ and $UV$ this two sides include $\angle V$

Step-by-step explanation:

Given;

A triangle $WVU$

We can see the figure of the triangle $WVU$

Where the $\angle V$ or $\angle WVU$ made by two sides $WV$ and $UV$ .

So $WV$ and $UV$ this two sides include $\angle V$

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3 years ago

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GaryK [48]

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3 years ago

A suitcase must weigh less than 50 pounds, or an extra fee will be charged. Patrick’s suitcase now weighs 38 pounds. How much we

Dvinal [7]

Answer:

Step-by-step explanation:

50 - 38 = 12

8 0

3 years ago