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MATHEMATICS Convergent sequence
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Exercise 27: Find
.Solution: We multiply and divide by the expression
. We have
.
Using the formula of (a - b) * (a + b) = a2 - b2 . We get
.
In the denominator we exclude from the bracket n . (Remember that in order to divide the square root of n express of root be divided by n2 ). We have.
The sequence
converges
to 0 ( Using the theotem: If
is a real number, then
)
.
Therefore
.