Question

The value of limₙtₒᵢₙfty(1+2+3+⋯+n)/(n²+100) is equal to:

• A. \(\infty\)
• B. \(\dfrac{1}{2}\)
• C. \(2\)
• D. 0

Hint:

Compare highest powers of n in limits at infinity.

Answer 1

The Correct Option is B

Step 1: 1+2+⋯+n=(n(n+1))/(2)
Step 2: ((n(n+1))/(2))/(n²+100) =(n²+n)/(2n²+200)
Step 3: Divide by n²: limₙtₒᵢₙfty(1+(1)/(n))/(2+(200)/(n²))=(1)/(2)