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andu1854
 one year ago
Use the Integral test to determine if the series shown below converges or diverges. Be sure to check that conditions of the integral test are satisfied.
Infinity Sigma n =1 for 7/(n^2 +25)
I understand that this does converge, but I need help trying to calculate where this converges to
andu1854
 one year ago
Use the Integral test to determine if the series shown below converges or diverges. Be sure to check that conditions of the integral test are satisfied. Infinity Sigma n =1 for 7/(n^2 +25) I understand that this does converge, but I need help trying to calculate where this converges to

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andu1854
 one year ago
Best ResponseYou've already chosen the best response.0dw:1437979024641:dw

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.2\[\large \sum\limits_{n=1}^{\infty}~\dfrac{7}{n^2+25}\] like that ?

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.2Integral test tells us this : If \(\int\limits_1^{\infty} \dfrac{7}{x^2+25}\,dx\) converges, then the given series also converges

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.2so evaluate the integral and see if it converges (finite)

Astrophysics
 one year ago
Best ResponseYou've already chosen the best response.1You also have to check the rules right, \[f(x) = \frac{ 7 }{ x^2+25 }\] is continuous on [1, infinity) then f(x) is positive. You also need to check if f is decreasing on [1, infinity) you can do this by taking the derivative, then if all those agree, you must evaluate the integral.

Astrophysics
 one year ago
Best ResponseYou've already chosen the best response.1Hint: \[\int\limits \frac{ 1 }{ x^2+a^2 } dx = \frac{ 1 }{ 2 } \tan^{1}\left( \frac{ x }{ a } \right)+C\]

andu1854
 one year ago
Best ResponseYou've already chosen the best response.0Ok so I understand that this will converge: so would it be 1/2 tan ^1 (1/5) then?

andu1854
 one year ago
Best ResponseYou've already chosen the best response.0ok then would I multiply this by 7 because 7 is the constant?

andu1854
 one year ago
Best ResponseYou've already chosen the best response.0ok I did this and got .69 ( rounded to nearest 100th)... so what would I do next...

Astrophysics
 one year ago
Best ResponseYou've already chosen the best response.1No, your result is wrong, it's an improper integral..

Astrophysics
 one year ago
Best ResponseYou've already chosen the best response.1\[\int\limits_{0}^{\infty} \frac{ 7 }{ x^2+25 } dx \]

andu1854
 one year ago
Best ResponseYou've already chosen the best response.0Ok its positive, it is continuous and it is decreasing as we move towards infinity... so:dw:1437984135224:dw

andu1854
 one year ago
Best ResponseYou've already chosen the best response.0dw:1437984288640:dw

andu1854
 one year ago
Best ResponseYou've already chosen the best response.0because the series starts at n =1, I felt a should be = 1 and b = inifinity
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