# Infinite limit of inverse tangent series

• flyerpower
In summary, the conversation discusses finding the infinite limit of a given sequence by using the formula (tanA - tanB)/(1 + tanAtanB) and identifying suitable values for A and B. The final solution is found to be arctan(1/x).
flyerpower

## Homework Statement

Take the infinite limit of that sequence.
(click to expand)

## The Attempt at a Solution

I have no idea where to start from, hints and ideas would be greatly appreciated.

Thanks.

hi flyerpower!

hint: (tanA - tanB)/(1 + tanAtanB)

tiny-tim said:
hi flyerpower!

hint: (tanA - tanB)/(1 + tanAtanB)

Ok, so tan(A-B)=(tanA-tanB)/(1+tanAtanB)

and A-B=arctan[(tanA-tanB)/(1+tanAtanB)

Now i think i should find some A and B so as :

tanA-tanB=x
and
tanA*tanB=k(k+1)*x^2

buuut i cannot still figure out what A and B should be

How about tan(A) =(k+1)x & tan(B) =kx ?

LOL, it was so obvious, thank you:)

It gives me pi/2 - arctg(x) which is arctg(1/x)

Thank you both!

## What is an infinite limit of inverse tangent series?

An infinite limit of inverse tangent series is a mathematical concept where the sum of an infinite number of terms in an inverse tangent series is evaluated. This type of series is also known as an arctangent series.

## How is an infinite limit of inverse tangent series calculated?

An infinite limit of inverse tangent series is calculated by taking the sum of an infinite number of terms in an inverse tangent series and evaluating it as the number of terms approaches infinity. This can be done using various mathematical techniques, such as the limit definition or the ratio test.

## What is the convergence of an infinite limit of inverse tangent series?

The convergence of an infinite limit of inverse tangent series depends on the value of the argument (input) of the inverse tangent function. If the argument is within a certain range, the series will converge and have a finite value. If the argument is outside of this range, the series will diverge and have an infinite value.

## What is the significance of an infinite limit of inverse tangent series in mathematics?

An infinite limit of inverse tangent series has many applications in mathematics, including in the study of complex numbers, trigonometry, and calculus. It is also useful in solving various mathematical problems, such as calculating the value of integrals and evaluating infinite sums.

## Are there any real-life applications of an infinite limit of inverse tangent series?

Yes, an infinite limit of inverse tangent series has practical applications in fields such as physics, engineering, and computer science. It is used to model and solve various real-world problems involving oscillations, vibrations, and electrical circuits.

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