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Infinite Series

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Mathematics
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Name
Infinite series with Maple
Exercise solutions
1) 1/2. The series converges and the sum is 1/2, the summation of this series starts at 1 and
not 0. The answer remains the same when calculated manually.
2) A). infinity b). 4
c). 0 d). 53.2456527
3) The summation is 3.14 which is pi (22/7). The series converges with a sum pi
2
/3; the
series has to sum up all the reciprocals of the positive integer squares.
Explanation
1. you take the limit as n approaches infinity for the equation
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
Replacing n with infinity it will give infinity because it will be 1 over infinity. Hence the
total sum will be 0.5.
2.
A. The total summation is infinity. Because as the power increases the value of the number
increase hence the total sum will be very large meaning infinity.




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B. You find the limit as n approaches infinity. Since n is on the power side, as it increases
the value of the answer also increase. The total summation from 1 to infinity will be 4.
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C. For this part, 1 raised to any number is 1. But as the power increase to infinity, the total
sum of the values gives zero. This is because infinity in just nothing and cannot be
defined.
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

D. The answer to this part is 53.2456527. Normally exponent (e) raised to infinity is infinity,
but in this case it has other factor. This make it not to be infinity. The total summation
from 0 to infinity is 53.2456527
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

3. The limit as n approaches infinity gives infinity but in this case it is squared hence not
infinity. Again the solution has a square root and therefore the square root of the total
summation is constant pie.




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Name Infinite series with Maple Exercise solutions 1) 1/2. The series converges and the sum is 1/2, the summation of this series starts at 1 and not 0. The answer remains the same when calculated manually. 2) A). infinity b). 4 c). 0 d). 53.2456527 3) The summation is 3.14 which is pi (22/7). The series converges with a sum pi2 /3; the series has to sum up all the reciprocals of the positive integer squares. Explanation 1. you take the limit as n approaches infinity for the equation 1 1 ) =0 lim ( 𝑛→∞ 𝑛2 + 3𝑛 + 2 Replacing n with infinity it will give infinity because it will be 1 over infinity. Hence the total sum will be 0.5. 2. A. The total summation is infinity. Because as the power increases the value of the number increase hence the total sum will be very large meaning infinity. −4 𝑛 lim ( ) = 0 𝑛→∞ 3 B. You find the limit as n approaches infinity. ...
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