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3 years ago

Evaluate the infinite sum

Mathematics

2 answers:

kkurt [141]3 years ago

7 0

Answer:

It does not converge.

Step-by-step explanation:

Given is an infinite geometric series whose first term is a = 4/7 and common ratio is r = 7/6.

The series ∑a·rⁿ converges if we have |r| < 1.

And the series ∑a·rⁿ diverges if we have |r| > 1.

But we can easily check that |r| = 7/6 > 1.

It means the given series diverges, i.e. does not converge.

Hence, option D is correct answer, i.e. It does not converge.

larisa [96]3 years ago

6 0

Answer:

D. it does not converge

You might be interested in

Calcula y comprueba las ecuaciones: porfavor alguienn la nesesito pliss a) 2X = 6 b) 10 + Z = 20 c) P + 9 = 11 d) 3X + 8 = + 29

Alexeev081 [22]

Answer:

a) x = 3

b) z = 10

c) p = 2

d) x = 7

e) u = 1

Step-by-step explanation:

a) 2x = 6

Despejamos x dividiendo por 2 a amabos lados de la eacuacion.

(2/2)x = 6/2

x = 3

Si remplazamos x en la ecuación original:

2(3)=6

6 = 6

Queda demostrado.

b) 10 + z = 20

Despejamos z restando 10 en amabos lados de la eacuacion.

10-10+z = 20-10

z = 10

Si remplazamos z en la ecuación original:

10 + 10=20

20 = 20

Queda demostrado.

c) p + 9 = 11

Despejamos p restando 9 en amabos lados de la eacuacion.

p + 9 - 9 = 11-9

p = 2

Si remplazamos p en la ecuación original:

2 + 9 = 11

11 = 11

Queda demostrado.

d) 3x + 8 = 29

Despejamos x restando 8 en amabos lados de la eacuacion y luego divideindo por 3 en ambos lados de la ecuación.

3x+8-8 = 29-8

3x = 21

(3/3)x = 21/3

x = 7

Si remplazamos x en la ecuación original:

3(7) + 8 = 29

21 + 8 = 29

29 = 29

Queda demostrado

e) 2u + 8 = 10

Despejamos u restando 8 en amabos lados de la eacuacion y luego divideindo por 2 en ambos lados de la ecuación.

2u+8-8 = 10-8

2x = 2

(2/2)x = 2/2

x = 1

Si remplazamos x en la ecuación original:

2(1) + 8 = 10

2 + 8 = 10

10 = 10

Queda demostrado

Espero te haya sido de ayuda!

5 0

3 years ago

Find the distance between the point - 3, 2 and 1 - 1

dusya [7]

Answer:

5 units

Step-by-step explanation:

Find the distance between the point - 3, 2 and 1 - 1

Given data

x1= -3

y1= 2

x2= 1

y2= -1

The expression for the distance between two points is

d=√((x_2-x_1)²+(y_2-y_1)²)

subtitute

d=√((1-(-3))²+(-1-(2))²)

d=√((1+3))²+(-1-2))²)

d=√((4)²+(-3))²)

d=√16+9

d=√25

d=5

Hence the distance between the points is 5 units

7 0

3 years ago

5) Find the common ratio and the next term. 512, 128, 32, 8,

serious [3.7K]

Answer:

The common ratio is $\frac{1}{4}$

The next term in the sequence is 2

Step-by-step explanation:

In a geometric sequence, the common ratio is the constant value you multiply a term by in order to find the value of the following term. Therefore, it is mathematically calculated as the quotient between a term and the term immediately before it. And it is in fact That is:

common ratio $r=\frac{a_{n+1}}{a_n}$