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4c0
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Homework Statement
Find limit of sequence An=(1-1/3)(1-1/6)...(1-1/(n(n+1)/2))
Homework Equations
The Attempt at a Solution
I just found limit of 1-1/(n(n+1)/2) when n→∞,which is 1.Is that a proper solution?
4c0 said:Homework Statement
Find limit of sequence An=(1-1/3)(1-1/6)...(1-1/(n(n+1)/2))
Homework Equations
The Attempt at a Solution
I just found limit of 1-1/(n(n+1)/2) when n→∞,which is 1.Is that a proper solution?
Homework Statement
Homework Equations
The Attempt at a Solution
A sequence is a list of numbers in a specific order. The limit of a sequence is the number that the sequence approaches as the index approaches infinity.
To find the limit of a sequence, we can use the formula: limit = 1/(1-r), where r is the common ratio of the sequence. In this case, the common ratio is 1/2, so the limit is 2.
The formula for finding the limit of a geometric sequence is: limit = 1/(1-r), where r is the common ratio of the sequence.
The limit of a sequence can be proven by showing that for any positive number ε, there exists a natural number N such that for all n>N, the absolute value of the difference between the limit and the nth term of the sequence is less than ε.
No, the limit of a sequence must be a real number or positive or negative infinity. It cannot be imaginary or undefined.