<p>The limit limx→∞
(x+1)10+(x+2)10+···+(x+100)10
x10+1010
is:</p>
Step-by-Step Solution
Key Concept: For limits at infinity, the ratio of the coefficients of the highest power of x determines the result.
<p><strong>1</strong>: The highest power in the numerator is x10. There are 100 such terms (from k = 1 to 100).</p><p><strong>2</strong>: Coefficient of x10 in numerator sum = 100.</p><p><strong>3</strong>: Coefficient of x10 in denominator = 1.</p><p><strong>4</strong>: Limit = 100/1 = 100.</p>
Correct Answer: 2