Consider the following recursive definition of a set S: 2,3, and 4 are members of S, so is 6 added to any member of S. Consider
the n'th finite approximation of the recursive definition of S. Prove using the first mathematical induction that, for all n >
1 answer:
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Answer:
T ' = √2 T
Step-by-step explanation:
Given that
Time period = P
Frequency = T
We know that time period for pendulum given as
When the length become half then time period will become p'
L'=L/2
It means that time period will become 0.707 P.
We know that frequency T
T= 1 /P
T' = 1/P'
T'=√2/P
T ' = √2 T
The key thing to look for to determine whether a sequence is geometric is to see whether the ratio between consecutive terms - the number I would multiply one term by to get the next - is constant.
By inspection, we see that the fourth answer choice satisfies that, as Why not the first? We have
The third choice is not a geometric sequence, but rather an arithmetic sequence, where the difference between consecutive terms is constant. Just to make sure that it isn't geometric, we compute
The second sequence is not geometric (although it does eventually converge to 1, but not its corresponding series), as