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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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Our hearts beat approximately 70 times per minute. Express in scientific notation how many times the heart beats over a lifetime
earnstyle [38]

Answer:

2.69 x 10^{9}

Step-by-step explanation:

We are given the heart's speed - 70 bpm

We count the number of minutes in 73 years :

  • 1 year = 365 days
  • 1 day = 24 hours
  • 1 hour = 60 minutes
  • 73 x 365 x 24 x 60 = 38,368,800 minutes

We multiply the heart's bpm with 73 years worth of minutes

38,368,800 x 70 = 2,685,816,000

Write the number in scientific notation = 2.68581 x 10^{9} ≈ 2.69 x 10^{9}

7 0
3 years ago
Draw graphs of the following lines: The line through the origin having a slope of 1/4
KengaRu [80]
I think its 1 on the graph correct me if im wrong
4 0
3 years ago
Explain how the commutative property of addition,the Associative property of addition and mental math can help you find 75.2+(57
4vir4ik [10]

Answer: The sum of 75.2+(57.376+24.8) is 157.376.

Explanation:

The commutative property of addition states that,

a+b=b+a

The associative property of addition states that,

a+(b+c)=(a+b)+a

The given expression is 75.2+(57.376+24.8).

First use commutative property of addition in the parenthesis.

75.2+(57.376+24.8)=75.2+(24.8+57.376)

Now use associative property of addition.

75.2+(24.8+57.376)=(75.2+24.8)+57.376

Now simplify the expression,

(75.2+24.8)+57.376=100+57.376

(75.2+24.8)+57.376=157.376

Therefore, the sum of 75.2+(57.376+24.8) is 157.376.

7 0
3 years ago
Read 2 more answers
The coordinates of the points below represents the vertics of a rectangle
Tanya [424]

Not sure what the question is, but I'm guessing you want to find out the area of the rectangle.

The distance between points P and Q is 4.

The distance between points Q and R is 3.

So the area is 3 * 4 = 12.

6 0
3 years ago
Whats a method you can use for times tables?
Sholpan [36]
For the 9 times table, in the answer section, order the answers 9,1,2,3,4,5,6,7,8,9 and then backwards order 0,1,2,3,4,5,6,7,8. This is a very easy way to understand the 9 times table.
4 0
3 years ago
Read 2 more answers
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