Definite Integration
Grade None
Question:
<p>Infinite rectangles each of width 1 unit and height <span class="math-tex">\(\left(\frac{1}{n}-\frac{1}{n+1}\right)(n \in N)\)</span> are constructed such that ends of exactly one diagonal of every rectangle lies along the curve y = <span class="math-tex">\(\frac{1}{x}\)</span>. The sum of areas of all such rectangles, is :</p>
<p style="display:inline"><span class="math-tex">\(\frac{1}{2}\)</span></p>
<p style="display:inline">1</p>
<p style="display:inline"><span class="math-tex">\(\frac{2}{3}\)</span></p>
<p style="display:inline"><span class="math-tex">\(\frac{3}{4}\)</span></p>
Step-by-Step Solution
Key Concept: The total area is calculated by summing the areas of the rectangles, which results in a telescoping series where intermediate terms cancel out.
<p>1</p>
Correct Answer: B