Which property is illustrated, 1n = n
1 answer:
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Given:
The arithmetic sequence is:
10, 12, 14, 16, ...
To find:
The function that generates the given sequence if n is an integer.
Solution:
We have,
10, 12, 14, 16, ...
Here, the first term is 10 and the common difference is:
The nth term of an arithmetic sequence is:
Where, a is the first term, d is the common difference and .
Putting in the above formula, we get
Therefore, the function generates the sequence.
Answer:
See answer below
Step-by-step explanation:
Define the intervals:
for n≥1.
The intervals are nested, in the sense that To see this, use the fact that for all n≥1, -1/n≤-1/(n+1) and 1/n≥1/(n+1) (intuitively, the intervals are "shrinking" in size, and are centered around √2).
The only point common to all intervals is √2, in the sense that
The idea for this construction is to center the intervals around √2 and shrink their size with the summand 1/n. As n goes to infinity, 1/n tends to zero and the intervals became closer and closer to √2, but they NEVER degenerate to the point √2, in contrast to their intersection.