Squares Built on Chords
Difficulty: Medium · Topics: Calculus, Series, Geometry
Vatarlarga qurilgan kvadratlar
For a natural number n, the curve y=x^2-2nx-2n meets the line y=x+1 at the two points P n and Q n. Let a n be the area of the square having the segment P nQ n as a diagonal.
What is the value of Σ n=1^∞frac1a n?
Natural n son uchun y=x^2-2nx-2n egri chiziq y=x+1 to‘g‘ri chiziqni ikki P n va Q n nuqtada kesadi. a n — diagonali P nQ n kesma bo‘lgan kvadrat yuzi bo‘lsin.
Σ n=1^∞frac1a n ning qiymati nechaga teng?