Experiments you can run yourself.
The ratio of consecutive Fibonacci terms tends to the golden ratio φ≈1.618.
Ever more frequent compounding gives capital that approaches a constant e-fold value, not one growing without bound.
The sum of infinitely many segments ½+¼+⅛+… equals exactly 1.
The sum 1+½+⅓+¼+… (out to infinity) is infinite — a divergent series.
A continuous function with f(a)<0 and f(b)>0 on [a,b] must have a root.
The tangent (Newton) method converges to a root very fast.
The sum 1+1/4+1/9+… is finite and equal to π²/6 ≈ 1.645.
The number of spirals in a sunflower head is usually a pair of consecutive Fibonacci numbers.
The sum 1+2+3+4+... is assigned (in the sense of regularization) the value -1/12.
A solid with a finite volume can have an infinite surface area.
The fastest descent from A to B is not a straight line, but a cycloid.
A freely hanging chain forms a catenary curve (cosh), not a parabola.