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True [87]
3 years ago
13

What is another pattern for 2,3,6,7,14,15,30,31,62,63,126,127

Mathematics
1 answer:
lana [24]3 years ago
3 0
127,126,63,62,31,30,15,14,7,6,3,2
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Does the series converge or diverge? If it converges, what is the sum? Show your work. ∑ ∞ n = 1 − 4 ( − 1 / 2 ) n − 1
Mekhanik [1.2K]

Answer:

Step-by-step explanation:

Given the series,

∑ ∞ n = 1 − 4 ( − 1 / 2 ) n − 1

I think the series is summation from n = 1 to ∞ of -4(-1/2)^(n-1)

So,

∑ − 4 ( − ½ )^(n − 1). From n = 1 to ∞

There are different types of test to show if a series converges or diverges

So, using Ratio test

Lim n → ∞ (a_n+1 / a_n)

Lim n → ∞ (-4(-1/ 2)^(n+1-1) / -4(-1/2)^(n-1))

Lim n → ∞ ((-4(-1/2)^(n) / -4(-1/2)^(n-1))

Lim n → ∞ (-1/2)ⁿ / (-1/2)^(n-1)

Lim n→ ∞ (-1/2)^(n-n+1)

Lim n→ ∞ (-1/2)^1 = -1/2

Since the limit is less than 0, then, the series converge...

Sum to infinity

Using geometric progression formula

S∞ = a / 1 - r

Where

a is first term

r is common ratio

So, first term is

a_1 = -4(-½)^1-1 = -4(-½)^0 = -4 × 1

a_1 = -4

Common ratio r = a_2 / a_1

a_2 = 4(-½)^2-1 = -4(-½)^1 = -4 × -½ = 2

a_2 = 2

Then,

r = a_2 / a_1 = 2 / -4 = -½

S∞ = -4 / 1--½

S∞ = -4 / 1 + ½

S∞ = -4 / 3/2 = -4 × 2 / 3

S∞ = -8 / 3 = -2⅔

The sum to infinity is -2.67 or -2⅔

Check attachment for better understanding

3 0
3 years ago
How can you determine if a relation is a function?
Montano1993 [528]

Answer:

cause none of the x's will repeat

Step-by-step explanation:

4 0
2 years ago
Jane is 3 years older than mary, and mary is twice as old as kay. if kay is x years old, how old is jane?
krek1111 [17]
The answer is y = 2x + 3.

x - Kay's age
y - Jane's age
m - Mary's age

<span>Jane is 3 years older than Mary: y = m + 3
</span><span>Mary is twice as old as Kay: m = 2x
</span><span>
y = m + 3
m = 2x

Substitute m in the first equation:
y = 2x + 3
</span>
6 0
2 years ago
Read 2 more answers
5. Sean has 56 bills in his pockets. The bills are only fives and tens.
noname [10]

Answer:

He have 43 bills of 10 and 13 bills of 5

Step-by-step explanation:

5x + 10y = 495

x + y = 56

Isolate x:

x = 56 - y

Substitute in the first equation:

5(56 - y) +10y = 495

280 -5y +10 y = 495

5y = 495 -280

5y = 215

y = 215/5

y= 43

Now substitute the value of y to find x:

x = 56 - y

x = 56 - 43

x = 13

3 0
2 years ago
What is the answer for 0.33×104
My name is Ann [436]

0.33 x 104 = 34.32

but

0.33 x 10⁴  =  3,300 .


4 0
3 years ago
Read 2 more answers
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