Question

Let \((a_n)=n^2\) and \((b_n)=1+\frac{1}{n^2}\) be sequences of real numbers, then:

• A. Both ($\text{a}_\text{n}$) and ($\text{b}_\text{n}$) are convergent
• B. Both ($\text{a}_\text{n}$) and ($\text{b}_\text{n}$) are divergent
• C. ($\text{a}_\text{n}$) is convergent and ($\text{b}_\text{n}$) is divergent
• D. ($\text{a}_\text{n}$) is divergent and ($\text{b}_\text{n}$) is convergent

Hint:

- Any sequence that grows infinitely large (like \( n^k \) for \( k > 0 \)) is divergent.
- Any sequence where the variable \( n \) only appears in the denominator of a fraction with a constant numerator (like \( \frac{1}{n^k} \)) will converge to 0 as \( n \to \infty \).

Answer 1

The Correct Option is D