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Sergio [31]
3 years ago
11

Does this sum converge: show steps

Mathematics
1 answer:
ehidna [41]3 years ago
6 0

Answer:

Yes

Step-by-step explanation:

\sum_{n=1}^{\infty} e^{-\sqrt{n} } \\\sum_{n=1}^{\infty} (\frac{1}{e})^{\sqrt{n} }

If we say u = √n, then:

\sum_{u=1}^{\infty} (\frac{1}{e})^{u}

This is a geometric series.  Since |1/e| < 1, the series converges.

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The sum of two numbers is 40 and the difference of these numbers is 14. Write a system of equations to represent this scenario a
ExtremeBDS [4]

Answer:

26

Step-by-step explanation:

6 0
3 years ago
Read 2 more answers
In circle O, AD and BE are diameters. What is MAE?
liraira [26]

Answer:

132°

Step-by-step explanation:

∠AOB = ∠EOD = 3x ( vertical angles )

∠AOB + ∠BOC = 90, that is

3x + 0.5x + 34 = 90

3.5x + 34 = 90 ( subtract 34 from both sides )

3.5x = 56 ( divide both sides by 3.5 )

x = 16

∠AOE + ∠EOD = 180 ( straight angle )

∠AOE + 3x = 180

∠AOE + (3 × 16) = 180

∠AOE + 48 = 180 ( subtract 48 from both sides )

∠AOE = 132°



5 0
3 years ago
Read 2 more answers
What is the best estimate for the length of a baseball bat?​
vredina [299]

Answer:

42 inches

By regulation it may be no more than 2.75 inches (7.0 cm) in diameter at the thickest part and no more than 42 inches (1.067 m) in length.

Step-by-step explanation:

baseball bat - is a smooth wooden or metal club used in the sport of baseball to hit the ball after it is thrown by the pitcher.

length- a measure of distance.

3 0
3 years ago
Given cos 0 = 1/6 and angle 0 is in Quadrant IV, what is the exact value of sin 0 in
Vinil7 [7]

cos 0 = 1/6

1 - cos²0 = sin²0

sin²0 = 35/36

in quadrant IV (4) the cos is positive sin is negative.

sin0 = - √35/6

4 0
2 years ago
Nell's mortgage is $50,150 at 10 percent for 30 years.
Rasek [7]

Answer:

The correct option is a.

Step-by-step explanation:

It is given that Nell's mortgage is $50,150 at 10 percent for 30 years and she must pay $8.78 points per $1,000.

<u>EMI on $1000 is $8.78, so EMI on $1 is</u>

EMI on $1 = 8.78/1000 = 0.00878

<u>EMI on $50150 is</u>

<u>EMI on $50150 = 0.00878 x 50150 = 440.317 = 440.32</u>

Therefore the correct option is a.

Hope this help you! ^_^

7 0
3 years ago
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