$$ \begin{array}{l}x=5 \ 25+5\end{array} \begin{array}{l}25+5=4^{2}+5\end{array} $$ 22) Andullah claims that as $$ n $$ approaches infinity, the expressions $$ \frac{1}{n+5} $$ and $$ \frac{1}{n}+5 $$ approach same value. Is Abdullah's claim correct? Explain.

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To decide whether Abdullah’s claim is correct, we need to determine the limits of each expression as n approaches infinity.

1. For the expression 1/(n + 5):
   As n → ∞, the denominator (n + 5) becomes infinitely large, so
   limₙ→∞ 1/(n + 5) = 0.

2. For the expression (1/n) + 5:
   As n → ∞, 1/n approaches 0, therefore,
   limₙ→∞ (1/n) + 5 = 0 + 5 = 5.

Since the first expression approaches 0 and the second approaches 5, Abdullah’s claim that they approach the same value is incorrect.
As n becomes very large, 1/(n + 5) approaches 0, while (1/n) + 5 approaches 5. Therefore, Abdullah's claim is incorrect because the two expressions do not approach the same value.

\[ \begin{array}{l}x=5 \\ 25+5\end{array} \begin{array}{l}25+5=4^{2}+5\end{array} \] 22) Andullah claims that as \( n \) approaches infinity, the expressions \( \frac{1}{n+5} \) and \( \frac{1}{n}+5 \) approach same value. Is Abdullah's claim correct? Explain.

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