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Andrews [41]
3 years ago
10

Find the limit of the sequence of partial sums whose general term is

D%7Bn%21%7D" id="TexFormula1" title="a_n=\frac{100^n}{n!}" alt="a_n=\frac{100^n}{n!}" align="absmiddle" class="latex-formula">
10

1

DNE

0

I am torn between the limit not existing and it being = 0.

Thank you so much.
Mathematics
1 answer:
nasty-shy [4]3 years ago
7 0

Answer:

0

Step-by-step explanation:

If ∑aₙ converges, then lim(n→∞)aₙ = 0.

Using ratio test, we can determine if the series converges:

If lim(n→∞) |aₙ₊₁ / aₙ| < 1, then ∑aₙ converges.

If lim(n→∞) |aₙ₊₁ / aₙ| > 1, then ∑aₙ diverges.

lim(n→∞) |(100ⁿ⁺¹ / (n+1)!) / (100ⁿ / n!)|

lim(n→∞) |(100ⁿ⁺¹ / (n+1)!) × (n! / 100ⁿ)|

lim(n→∞) |(100 / (n+1)|

0 < 1

The series converges.  Therefore, lim(n→∞)aₙ = 0.

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In the rhombus, m angle 1 = 18x, m angle 2 = x+y and m angle 3 = 30z. Find the value of x+y+z. The diagram is not drawn to scale
Ratling [72]

The value of x+y+z = 93

<u>Explanation:</u>

<u></u>

angle 1 = 18x

angle 2 = x+y

angle 3 = 30z

In rhombus, the diagonals intersect at 90°

Therefore,

angle 1 : 18x = 90

                  x = 90/18 = 5

angle 2: x+y = 90

              5+y = 90

                  y = 85

angle 3: 30z = 90

                   z = 90/30 = 3

Value of x+y+z = 5+85+3 = 93

Thus, the value of x+y+z = 93

             

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Answer:

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Step-by-step explanation:

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**pretend ∈ is the sum symbol

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Mass of left part = lim x->0 ∈ (1+x)*y*deltax = inegral 0 to 1 of (1+x)*3*(-x+1) = 3 * integral 0 to 1 of (-x^2 + 1) = 3 * 2/3 = 2

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8 0
3 years ago
On a baseball field, the pitcher’s mound is 60.5 feet from home plate. During practice, a batter hits a ball 195 feet at an angl
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In this problem, we can imagine that all the points connect to form a triangle. The three point or vertices are located on the pitcher mount, the home plate and where the outfielder catches the ball. So in this case we are given two sides of the triangle and the angle in between the two sides.

<span>With the following conditions, we can use the cosine law to solve for the unknown 3rd side. The formula is:</span>

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<span>Therefore the outfielder throws the ball at a distance of 147.23 ft towards the home plate.</span>

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