Answer: You will never reach a sum of 2. You would need infinitely many terms to sum up.
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Explanation:
We have this sequence
1, 1/2, 1/4, 1/8, 1/16, 1/32, 1/64, ...
which is geometric with the following properties
- a = first term = 1
- r = common ratio = 1/2 = 0.5
Notice how we multiply each term by 1/2 to get the next term. Eg: (1/4)*(1/2) = 1/8 or (1/16)*(1/2) = 1/32.
Since r = 0.5 is between -1 and 1, i.e. -1 < r < 1 is true, this means that adding infinite terms of this form will get us to approach some finite sum which we'll call S. This is because the new terms added on get smaller and smaller.
That infinite sum is
S = a/(1-r)
S = 1/(1-0.5)
S = 1/0.5
S = 2
So if we keep going with that pattern 1+1/2+1/4+... and do so forever, then we'll reach a sum of 2. However, we cannot go on forever since it's asking when we'll reach that specific sum. In other words, your teacher wants finitely many terms to be added.
In short, we'll never actually reach the sum 2 itself. We'll just get closer and closer.
Here's a list of partial sums
- 1+1/2 = 1.5
- 1+1/2+1/4 = 1.75
- 1+1/2+1/4+1/8 = 1.875
- 1+1/2+1/4+1/8+1/16 = 1.9375
- 1+1/2+1/4+1/8+1/16+1/32 = 1.96875
- 1+1/2+1/4+1/8+1/16+1/32+1/64 = 1.984375
- 1+1/2+1/4+1/8+1/16+1/32+1/64+1/128 = 1.9921875
- 1+1/2+1/4+1/8+1/16+1/32+1/64+1/128+1/256 = 1.99609375
We can see that we're getting closer to 2, but we'll never actually get there. We'd need to add infinitely many terms to get to exactly 2.
Complete Question
A sensor output was acquired for 32 seconds at a rate of 200 Hz and spectral analysis was performed using FFT. If the data set was split into 5 segments (each 6.4 seconds long), what is the resulting:
a)F minimum
b) F maximum
c) Frequency resolution
Answer:
a) 
b) 
c) 
Step-by-step explanation:
From the question we are told that:
Time 
Frequency
Segments 
Generally the equation for Frequency Range is mathematically given by
Therefore
a)
b)
c)
Generally the equation for Frequency Resolution is mathematically given by
Where
N=The Total dat points
N=Sampling Frequency *Time
Therefore
Answer:
Result = 124.6
Step-by-step explanation:
If the digit after tenth is greater than or equal to 5, add 1 to tenth. Else remove the digit. Example
124.58
The first number of right of decimal point is 5
The second digit after decimal point is 8 which is greater than 5
So add 1 to 5
Result = 124.6
Answer:
The answer is given below <3
Step-by-step explanation:
The options are not given but I would list the inequalities needed to solve this problem.
As a result of increase in people to attend meeting, the number of sushi needed to be ordered is 100 pieces. Sofia has already ordered 24 pieces. If R is the number of additional rolls that Sofia orders.
The number of additional rolls that Sofia orders (R) must be greater than or equal to the difference between the number of Sushi needed to be ordered and the number of Sushi that has already being ordered. It is given by the inequality:
R ≥ 100 - 24
R ≥ 76
If each roll contains 12 pieces, the number of rolls needed (n) is given by:
n ≥ R/12
n ≥ 76/12
n ≥ 6.33
n ≥ 7
If each roll cost $8, the money needed to buy the sushi is given as:
Cost ≥ 8(7) ≥ $56
