Monotone Convergence Theorem (Real Analysis)/Examples
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Examples of Use of Monotone Convergence Theorem (Real Analysis)
Example: $\dfrac {n - 1} n$
The sequence $\sequence {a_n}_{n \mathop \ge 1}$ defined as:
- $a_n = \dfrac {n - 1} n$
is convergent to the limit $1$.
Example: $x^n$ for $0 < x < 1$
Let $x \in \R$ such that $0 < x < 1$.
The sequence $\sequence {a_n}_{n \mathop \ge 1}$ defined as:
- $a_n = x^n$
is convergent to the limit $0$.