Consider expression :
1)
2)
3)
4)
Answer:
1 A polynomial expression of degree three is shown below.
2 answers:
Answer:
C:
Step-by-step explanation:
First of all, you need to be able to recognize the two terms as cubes, and what they are cubes of. In this case, and
.
Then you have to find a way you like to remember the formula for how to factorize. The way I do it is by saying "the binomial has the same zero as the original, so and
and the whole expression has one minus sign attached to the second term of either factor. In the sum of cubes first parenthesis has a plus, so the second term of the other parentesis has to take that minus:
while in the difference of cubes you already used a minus, so everything else goes plus:
Or you commit the two formulas to memory.
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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
