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MATHEMATICS Convergent sequence
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Exercise 49: Calculate the limit
Solution: By using the logarithmic function of (
,
for a > 0, a ®
1,
b > 0, J 5
§ ),
we can write
Since the function f(x) = log 3 (x) is a function of increasing (strictly increasing), that is log 3 (x) <log 3 (x +1), we can write
,
Similarly, we estimate, on the other hand, since the function f (x) = log 3 (x) is increasing, we can write
.