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Mathematics
Expand and evaluate the series n=5 ai=2×i^2+3
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P Answered by PhD
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Mathematics
5. evaluate the series 50 + 10 + 2 + . . 62 the series diverges; it does not have a sum. 62.5
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P Answered by PhD 7
62.5
Step-by-step explanation:
By dividing 50 by 10 and 10 by 2 we can find that r, or the common ratio is 1/5, meaning that this series converges, so it is solvable. The formula for a convergent series is . By plugging in 1/5 for r and 50 for
we can find that the sum of this infinite series is 62.5
Mathematics
the series has 8 terms.evaluate the series 1/2,3/2,5/2,…,15/2 you
Step-by-step answer
P Answered by PhD 1
This is an arithmetic sequence, not a series, (series are infinite, sequences are finite)because each term is a constant difference from the term preceding it, called the common difference.
Technically the sum of any arithmetic sequence is:
s(n)=(2an+dn^2-dn)/2
However the above equation is derived from the fact that the sum of an arithmetic sequence is the average of the first and last terms times the number of terms in the sequence.
All we really have to "solve" for then is the number of terms in the sequence...the rule for the sequence of an arithmetic sequence is:
a(n)=a+d(n-1), a=first term, d=common difference, n=term number. Since we know a=1/2 and d=1 we can solve for n...
a(n)=1/2+n-1
a(n)=n-1/2, now we just solve for n when a(n)=15/2
15/2=n-1/2
n=16/2
n=8 so there are seven terms, now we can say:
s(8)=8(1/2+15/2)/2
s(8)=32
Mathematics
The first five terms of a sequence are 2, 5/3, 3/2,7/5, and 4/3. Which of the following can be used to evaluate the series
Step-by-step answer
P Answered by Specialist 24
D.
I JUST TOOK THE TEST, PICTURE ATTACHED.
Mathematics
Evaluate the series 4-2 1-0.5 0.25 to s10. round to the nearest tenth. a. 5.50 b.-2.75 c.2.75 d. 2.66
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P Answered by Master 11
If we're talking about series, we're talking about a summation.
This is a geometric series, so we will be using the sum to n terms of a geometric series given by:
, where a is the first term, r is the common ratio, and n is the number of terms.
Now, we know the first term is 4.
We know the ratio is
And we are finding to the 10th term.
Plugging everything into the equation:
After this, we get: 2.6640625...≈ 2.66 (ie D)
Mathematics
Evaluate the series 4 – 2 + 1 – 0.5 + 0.25 to s10. round to the nearest hundredth.
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P Answered by PhD 6
The initial term of this geometric series is 4, and the common ratio is -1/2. The sum is given by
The sum is approximately 2.66.
Mathematics
Evaluate the series 4 – 2 + 1 – 0.5 + 0.25 to s10. round to the nearest hundredth.
Step-by-step answer
P Answered by PhD 6
The initial term of this geometric series is 4, and the common ratio is -1/2. The sum is given by
The sum is approximately 2.66.
Mathematics
We can use this power series to approximate the constant . a) First, evaluate arctan(1) . (You do not need the series to evaluate it.) b) Use your answer from part (a) and the power series above to find a series representation for . (The answer will be just a series – not a power series.) c) Verify that the series you found in part (b) converges. d) Use your convergent series from part (b) to approximate with |error| 0.5. e) How many terms would you need to approximate with |error| 0.001?
Step-by-step answer
P Answered by Specialist
(a)
(b)
(c)
Therefore if you sum any three terms of it you get the desired accuracy.
(d)
If you sum 1999 terms you get the desired accuracy.
Step-by-step explanation:
From the information given we know that
(a)
For that you need to find and angle such that
= 1, remember that
therefore
(b)
Then you just multiply by 4 and get that
(c)
Using the alternating series test, since the sequence is decreasing and its limit tends to 0 when n tends to infinity the series is convergent.
(d)
Using the estimation theorem of alternating series we know that if denotes the partial sum of the series then
Therefore we are looking for an such that
we just have to solve that inequality, when you solve that inequality you get that
Therefore if you sum any three terms of it you get the desired accuracy.
(e) For this part you need to solve the following inequality
When you solve that inequality you get that
so, if you sum 1999 terms you get the desired accuracy.
Mathematics
For the following telescoping series, find a formula for the nth term of the sequence of partial sums S n . Then evaluate lim n → [infinity] S n to obtain the value of the series or state that the series diverges. ∑ [infinity] k = 1 = 10 ( 5 k − 1 ) ( 5 k + 4 )
Step-by-step answer
P Answered by PhD
I'm guessing the sum is supposed to be
Split the summand into partial fractions:
If , then
If , then
This means
Consider the th partial sum of the series:
The sum telescopes so that
and as , the second term vanishes and leaves us with
Mathematics
For the following telescoping series, find a formula for the nth term of the sequence of partial sums {Sn}. Then evaluate Lim Sn to obtain the value of the series or state that the series diverges. n→[infinity] [infinity] Σ (4/√k+5 ) - 4/ √ k+6) k=1
Step-by-step answer
P Answered by PhD 1
Looks like the series is
This series has n-th partial sum
(where is used as a placeholder for the summand)
In each grouped term, the last term is annihilated by the first term of the next group; that is, for instance,
Ultimately, all the middle terms will vanish and we're left with
As , the last term converges to 0 and we're left with
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