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gladu [14]
3 years ago
9

Find the value of:

5Cfrac%7B1%7D%7B100%5E2%7D%29" id="TexFormula1" title="(1-\frac{1}{2^2})(1-\frac{1}{3^2})...(1-\frac{1}{100^2})" alt="(1-\frac{1}{2^2})(1-\frac{1}{3^2})...(1-\frac{1}{100^2})" align="absmiddle" class="latex-formula"> help ASAP

Mathematics
2 answers:
OLEGan [10]3 years ago
8 0
<h3>Answer:  101/200</h3>

==================================================

Explanation:

Each term multiplied out is of the form 1 - 1/(k^2) which we can write as 1^2 - (1/k)^2

Note we have something in the form a^2 - b^2 with a = 1 and b = 1/k

So  

a^2 - b^2 = (a-b)(a+b)

1^2 - (1/k)^2 = (1 - 1/k)(1 + 1/k)

1^2 - (1/k)^2 = [ (k - 1)/k ] * [ (k + 1)/k ]

----------------

Let P = [ (k - 1)/k ] * [ (k + 1)/k ]  represent the kth term we are dealing with

Then let Q be the term just after term P, so it's the (k+1) term

To form term Q, replace every k with k+1

Q =  [ (k+1 - 1)/(k+1) ] * [ (k+1 + 1)/(k+1) ]

Q = [ k/(k+1) ] * [ (k+2)/(k+1) ]

----------------

Let's multiply P and Q to find out what happens . See figure 1 in the attached images below.

As figure 1 shows, we see that the middle terms cancel out. This will happen when we multiply P*Q*R, where R is the term just after Q. Extend this idea out as far as you want and each time the middle terms will pair up and cancel.

All that's left are the first and last terms, which are

1 - 1/2 = 1/2

and

1 + 1/100 = 101/100

They multiply to 101/200

----------------

Figure 2 (also attached as an image) shows a longer way to do the problem. Basically I expanded out a bunch of terms to multiply, and then show how we have various terms pair up and cancel, in basically the same way as explained above. What's left are the first and last terms 1/2 and 101/100 which multiply to 101/200.

KonstantinChe [14]3 years ago
4 0

Answer

(1-1/2 2)= 3/4 <Exact Form>  0.75<Decimal Form>

1-(1)/(100^(2) = 9999/10000 <Exact Form> 0.9999 <Decimal Form>

Step-by-step explanation:

Hope this Helps! The Crystaline Gamerz on YT! Bye! please sub

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–2x + 2y = -4<br> 3х + Зу = -18
rodikova [14]

Answer:

(-2, -4)

Step-by-step explanation:

–2x + 2y = -4

3х + Зу = -18

Divide the first equation by 2

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Divide the second equation by 3

3х/3 + Зу/3 = -18/3

x + y = -6

Add these equation together

-x +y = -2

x + y = -6

-------------------

0x + 2y = -8

2y = -8

Divide each side by 2

2y/2 = -8/2

y = -4

Now we need x

x+y = -6

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3 0
3 years ago
BRAINLIEST GIVEN TO BEST ANSWER
lbvjy [14]

Answer:

Slope = \frac{1}{4}

Step-by-step explanation:

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From the graph attached,

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3 years ago
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Vinvika [58]
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6 0
3 years ago
A 36 ft tree casts a 9 ft shadow at the same time a building casts a 15 ft shadow. How tall is the building?
mote1985 [20]

Answer: The height of the tree is  27f t

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h/s

h/15=18/10

Cross multiply

10.h= 18*15

10h=270

Use the multiplicative Inverse

10 h/ 10 = <em><u>270 /10 =27</u></em>

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2 years ago
Evaluate the following expression if x= 2.14<br> 3.35x + 25 - 2x
prohojiy [21]

Answer:

The final answer is 27.889 (Feel free to round it)

Step-by-step explanation:

3.35 x 2.14 = 7.169

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32.169 - 4.28 = 27.889

Can I have brainliest? It would help me out, if not thanks anyways! Hope this helped and have a nice day!

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