Hola buenos días ayuda

For every integer k from 1 to 10, inclusive the "k"th term of a certain sequence is given by (−1)(k+1)∗(12k). If T is the sum of

Katena32 [7]

Answer:

Option D. is the correct option.

Step-by-step explanation:

In this question expression that represents the kth term of a certain sequence is not written properly.

The expression is $(-1)^{k+1}(\frac{1}{2^{k}})$ .

We have to find the sum of first 10 terms of the infinite sequence represented by the expression given as $(-1)^{k+1}(\frac{1}{2^{k}})$ .

where k is from 1 to 10.

By the given expression sequence will be $\frac{1}{2},\frac{(-1)}{4},\frac{1}{8}.......$

In this sequence first term "a" = $\frac{1}{2}$

and common ratio in each successive term to the previous term is 'r' = $\frac{\frac{(-1)}{4}}{\frac{1}{2} }$

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

Since the sequence is infinite and the formula to calculate the sum is represented by

$S=\frac{a}{1-r}$ [Here r is less than 1]

$S=\frac{\frac{1}{2} }{1+\frac{1}{2}}$

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

S = $\frac{1}{3}$

Now we are sure that the sum of infinite terms is $\frac{1}{3}$ .

Therefore, sum of 10 terms will not exceed $\frac{1}{3}$

Now sum of first two terms = $\frac{1}{2}-\frac{1}{4}=\frac{1}{4}$

Now we are sure that sum of first 10 terms lie between $\frac{1}{4}$ and $\frac{1}{3}$

Since $\frac{1}{2}>\frac{1}{3}$

Therefore, Sum of first 10 terms will lie between $\frac{1}{4}$ and $\frac{1}{2}$ .

Option D will be the answer.

3 0

3 years ago

Find the length of the missing side

inn [45]

<h3>Answer: 9</h3>

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Work Shown:

a = unknown = leg #1

b = 12 = leg #2

c = 15 = hypotenuse

Plug those values into the pythagorean theorem and solve for 'a'

a^2 + b^2 = c^2

a^2 + (12)^2 = (15)^2 .... substitution

a^2 + 144 = 225

a^2 = 225 - 144 ... subtracting 144 from both sides

a^2 = 81

a = sqrt(81) .... applying square root to both sides

a = 9

7 0

3 years ago

Determine which of the following situations requires the distributive property in order to simplify the expression. Select all s

ipn [44]

Answers

9(x + y)

(7 - a)(b)

The Distributive Property is used in algebraic expressions to multiply a single term and two or more terms which are inside a set of parentheses.

In the case of x(2y), there is only one term inside the parenthesis

In the case of 9(x ∙ y), the distributive property is not used because (x ∙ y) = xy which means only one term will be multiplied by the term outside the parenthesis (9)

In the case of 9(x + y), the distributive property is used because the two terms in the parenthesis (x and y) will be multiplied by the term outside the parenthesis (9)

9(x + y) = 9*x + 9*y (by applying the distributive property)

In the case of (7 ∙ a)(b), the distributive property is not used because (7 ∙ a) = 7a which means only one term will be multiplied by the term outside the parenthesis (b)

In the case of (7 - a)(b), the distributive property is used because the two terms in the parenthesis (7 and -a) will be multiplied by the term outside the parenthesis (b)

(7 - a)(b) = 7*b - a*b (by applying the distributive property)

In the case of (2 ∙ x) ∙ y, the distributive property is not used because (2 ∙ x) = 2x which means only one term will be multiplied by the term outside the parenthesis (y)

8 0

3 years ago

Read 2 more answers

Simplify: -0.8b + 4.1c -(-3.2b) - 0.1c

umka21 [38]

-0.8b+4.1c-(-3.2b)-0.1c
-(-3.2b)= 3.2b
4.1c-0.1c=4c
-0.8b+4c+3.2b
-0.8b+3.2b=2.4b

4c+2.4b

3 0

2 years ago

Read 2 more answers

3 Terrence uses pieces of wood that are 10 inches long to

Alchen [17]

Answer:

146 whistles

Step-by-step explanation:

First, convert 122 feet to inches, by multiplying it by 12

122(12)

= 1464

Divide this by 10 to find how many whistles he can make

1464/10

= 146.4

Since we can only have a whole number of whistles, we have to round down to 146.

So, he can make 146 whistles

3 0

2 years ago

Hola buenos días ayuda​

Hola buenos días ayuda