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Problem
Problem
The value of
lim
n
→
∞
(
n
2
+
n
+
1
−
⌊
n
2
+
n
+
1
⌋
)
\lim_{n \to \infty} \left(\sqrt{n^2 + n + 1} - \left\lfloor \sqrt{n^2 + n + 1} \right\rfloor\right)
lim
n
→
∞
(
n
2
+
n
+
1
−
⌊
n
2
+
n
+
1
⌋
)
where
⌊
⋅
⌋
\lfloor \cdot \rfloor
⌊
⋅
⌋
denotes the greatest integer function is a. 0 b. 1/2 c. 2/3 d. 1/4
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