Daily Math · 2026-06-05

Question 1

The sum $1 + 2 + 3 + \cdots + 100$ equals:

Accepted Answer

Apply the formula $\dfrac{n(n+1)}{2} = \dfrac{100 \cdot 101}{2} = 5050$.

Answer

$5050$

Answer

$5000$

Answer

$10000$

Answer

$4950$

Question 2

The middle term of the expansion of $(x + 1)^8$ has coefficient:

Accepted Answer

Middle coefficient: $\binom{8}{4} = 70$.

Answer

$28$

Answer

$56$

Answer

$70$

Answer

$128$

Question 3

The limit $\displaystyle\lim_{x 	o 1} \dfrac{x^3 - 3x + 2}{x - 1}$ equals (apply Bezout / factoring):

Accepted Answer

$x^3 - 3x + 2 = (x - 1)(x^2 + x - 2) = (x - 1)(x - 1)(x + 2) = (x - 1)^2 (x + 2)$. So $\dfrac{(x-1)^2(x+2)}{x - 1} = (x - 1)(x + 2) 	o 0$ as $x 	o 1$.

Answer

$0$

Answer

$1$

Answer

$3$

Answer

$\infty$

Problems & worked solutions

Problem 1 — Sequences

Problem 2 — Binomial Theorem

Problem 3 — Limits of Functions