Step-by-step explanation:
These are all examples of p-series:
∑(1 / nᵖ), where p>0.
If p > 1, the series converges. If 0 < p ≤ 1, the series diverges.
First option:
∑(1/n⁵)
Here, p = 5. Since 5 > 1, the series converges.
Second option:
∑((√n+3)/n³)
∑((√n)/n³) + ∑(3/n³)
∑(1/n^2.5) + 3 ∑(1/n³)
In the first sum, p = 2.5. In the second sum, p = 3. Both are greater than 1, so the series converges.
Third option:
∑((n−4)/(n⁴√n))
∑(1/(n³√n)) − ∑(4/(n⁴√n))
∑(1/n^3.5) − 4 ∑(1/n^4.5)
In the first sum, p = 3.5. In the second sum, p = 4.5. Both are greater than 1, so the series converges.
Fourth option:
∑(1/∛n)
∑(1/n^⅓)
Here, p = ⅓. This is less than 1, so the series diverges.
Note: if a series is converging, then the limit is 0.
However, if the limit of a series is 0, it does not necessarily mean that series is converging.
Here, the limit of all 4 options is 0. However, the fourth option is a diverging series.
If 12 was remove from the data set, it will remain same
A boxplot is a graphical rendition of statistical data based on the minimum, first quartile, median, third quartile, and maximum.
According to the given topic the box plot represent the number of children in 30 different families.
and the value of 12 is remove for error.
so, if the median is 2 children for both the plots.
When 12 was remove from the data set, it will remain same
Learn more about box plot here:
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7x = 78
1.142 is the value of x in the equation 7x = 78.
The given equation is 7x = 78
In the equation x is the variable.
We need to find the value of x.
Divide both sides by 7 to get the value of x
x=78/7
x=11.142
Hence, the value of x in the equation 7x = 78 is 11.142.
To learn more on Equation:
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Answer:
There are 48 boys in the choir
Step-by-step explanation:
2(x + 14) = 2x + 28
B.
7x + 14 = −2x − 17
C.
2x + 14 = 2x + 14
D.
7x + 14 = 7x − 17
Answer:
Option A
Step-by-step explanation:
2(x+14)=2x+28
2x+28=2x+28
IT HAS REAL SOLUTION :)
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