Sequences & Series
Infinite Series
Grade 11
Question:
<p>The sum <span>\(\frac{1 \cdot 9}{1 \cdot 2 \cdot 3} + \frac{1 \cdot 28}{2 \cdot 3 \cdot 4} + \frac{1 \cdot 39}{3 \cdot 4 \cdot 5} + \frac{1 \cdot 522}{4 \cdot 5 \cdot 6} + \ldots\)</span> up to infinite terms is equal to</p>
<p>(A) ...</p>
<p>(B) 1</p>
<p>(C) 2</p>
<p>(D) 4</p>
Step-by-Step Solution
Key Concept: Recognize the series structure and use partial fractions to create a telescoping series.
<p>Use partial fractions to decompose the general term and find the sum telescopes to 1.</p>
Correct Answer: B