Multi-concept problems that turn intricate hurdles into intuitive solutions. Tap any problem to open it full-screen.
A nested sum with binomial coefficients and powers of 3 and 5, taken to infinity. The key is to collapse the inner sum with the binomial theorem first — the limit then reveals itself.
Tangents are drawn from a point on one ellipse to a concentric, similar ellipse. Prove that the normals at their points of contact meet on a third conic — a beautiful test of chord of contact and normal geometry.
Only the boundary values of f′ and a lower bound on f″ are known. Use these constraints cleverly to find the largest value the integral function g(x) can attain.
An integral from 0 to infinity of a rational function raised to a power. The right substitution turns it into a standard form and delivers the constant k.
Each square root looks daunting, yet every term is a perfect square in disguise. Spot the pattern, let the series telescope, and read off the digits of n.
An equation built from logarithms whose bases are sin²x and cos²x. Handle the domain restrictions and change of base carefully, then count the solutions in (−π, 2π).
