Daily Math · 2026-06-03

Question 1

Are the vectors $\vec{u} = \vec{i} + 2\vec{j}$ and $\vec{v} = 2\vec{i} + 4\vec{j}$ collinear?

Accepted Answer

$\vec{v} = 2\vec{u}$, so the two vectors are collinear (parallel).

Answer

Yes, $\vec{v} = 2\vec{u}$

Answer

No, the dot product is non-zero

Answer

Yes, but only because they are perpendicular

Answer

No, they have different magnitudes

Question 2

What is the sum of the infinite geometric series $1 + 	frac{1}{2} + 	frac{1}{4} + \cdots$?

Accepted Answer

Geometric series with $a=1$, $r=	frac{1}{2}$. Sum $= 	frac{a}{1-r} = 	frac{1}{1-1/2} = 2$.

Answer

$\dfrac{3}{2}$

Answer

$2$

Answer

$\dfrac{5}{2}$

Answer

Diverges

Question 3

$\displaystyle\sum_{k=1}^{99} \dfrac{1}{k(k+1)}$ equals:

Accepted Answer

The sum telescopes: $\sum_{k=1}^{99} \left(\dfrac{1}{k} - \dfrac{1}{k+1}\right) = 1 - \dfrac{1}{100} = \dfrac{99}{100}$.

Answer

$	frac{99}{100}$

Answer

$	frac{100}{99}$

Answer

$	frac{1}{100}$

Answer

$1$

Problems & worked solutions