22990atinesh said:Homework Statement
The value of ##\sqrt{12+\sqrt{12+\sqrt{12+ ...}}}## is
Homework Equations
The Attempt at a Solution
No Clue
Assign the entire sum as a variable.22990atinesh said:Homework Statement
The value of ##\sqrt{12+\sqrt{12+\sqrt{12+ ...}}}## is
Homework Equations
The Attempt at a Solution
No Clue
Ashes Panigrahi said:Assign the entire sum as a variable.
##\sqrt{12+\sqrt{12+\sqrt{12+ ...}}} = k##
##\Rightarrow 12+\sqrt{12+\sqrt{12+ ...}} = k^2## ... (1)
But,
##\sqrt{12+\sqrt{12+ ...}} = k## ...(2)
Substitute (2) in (1),
Then solve for ##k##.
22990atinesh said:Homework Statement
The value of ##\sqrt{12+\sqrt{12+\sqrt{12+ ...}}}## is
Homework Equations
The Attempt at a Solution
No Clue
An infinite series is a sum of an infinite number of terms. It is written in the form of a_n + a_(n+1) + a_(n+2) + ..., where a_n is the n-th term in the series.
There are different methods for finding the sum of an infinite series, depending on the type of series. One common method is to use the formula for the sum of a geometric series, which is given by S = a/(1-r), where S is the sum, a is the first term, and r is the common ratio. Another method is to use the technique of telescoping, where the terms in the series cancel each other out, leaving only a finite number of terms to be added.
The divergence test is a method used to determine if an infinite series diverges or converges. It states that if the limit of the terms in the series does not approach zero, then the series diverges. However, if the limit is equal to zero, the series may still converge.
Yes, there are some calculators that have a function for finding the sum of an infinite series. However, it is important to note that these calculators may not be able to handle all types of series, and it is always recommended to double check the answer using a different method.
There are several tests that can be used to determine the convergence of an infinite series, such as the comparison test, ratio test, and integral test. These tests compare the given series to a known series or function to determine if it behaves in a similar way. It is important to note that the tests only provide a sufficient condition for convergence, and further analysis may be needed to confirm convergence.