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MATHEMATICS Convergent sequence
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Exercise 39: Calculate the limit
.Solution: In calculating this limit we use the theorem of the three sequences, which find two sequences, one of the string about larger words from sequence
,
The second sequence of smaller words than
and if this sequences will be the same limit, then the sequence
will be corvengent, and it converges to the same limit.
Please, note that
,
so
.
Thus
.
We use the formula of
,
for a > 0.
Therefore
and
.
Using the theorm of the three sequences, the sequence (an) is convergent, and it converges to 0,8.