mathematics

Off-by-one in the count

What goes wrong

Counts the intervals where the stem counts the endpoints, or the reverse.

Next time

Explicitly state whether boundaries are included—use $(b - a + 1)$ for inclusive integer ranges—and list the edge cases ( $0$ , start, and end elements) by hand.

Questions that set this trap

9 published questions

mathematicsLet $g: R \rightarrow R$ be a non constant twice differentiable such that…
mathematicsLet $y=f(x)$ represent a parabola with focus $\left(-\frac{1}{2}, 0\right)$ and directrix $y=-\frac{1}{2}$ . Then…
mathematicsLet $a_1, a_2, a_3, \dots$ be an A.P. If $a_7 = 3$ , the product $a_1 a_4$ is minimum and the sum of its first $n$ terms is zero, then…
mathematicsThe number of points on the curve $y=54 x^{5}-135 x^{4}-70 x^{3}+180 x^{2}+210 x$ at which the normal lines are parallel to…
mathematicsIf $\mathrm{a}_{\mathrm{n}}=\frac{-2}{4 \mathrm{n}^{2}-16 \mathrm{n}+15}$ , then $\mathrm{a}_{1}+\mathrm{a}_{2}+\cdots+\mathrm{a}_{25}$ is e…
mathematicsIf $[t]$ denotes the greatest integer $\leq t$ , then the value of $\frac{3(e-1)}{e} \int_1^2 x^2 e^{[x]+[x^3]} dx$ is :
mathematicsLet $M$ be the maximum value of the product of two positive integers when their sum is 66. Let the sample space…
mathematicsLet $f(x) = 2x^n + \lambda, \lambda \in \mathbb{R}, n \in \mathbb{N}$ , and $f(4) = 133, f(5) = 255$ . Then the sum of all the positive integ…
mathematicsThe value of $\Sigma_{r=0}^{22}{ }^{22} \mathrm{C}_r{ }^{23} \mathrm{C}_r$ is