A Series of Remainders
Difficulty: Medium · Topics: Algebra, Series, Polynomials
Qoldiqlar qatori
For a real number a with a≠ 0 and a natural number n, let R n be the remainder when the polynomial x^3+x is divided by the linear polynomial a^nx-1.
If Σ n=1^∞R n=-4/9, what is the value of a?
a≠ 0 bo‘lgan haqiqiy a son va natural n son uchun R n — x^3+x ko‘phadni a^nx-1 chiziqli ko‘phadga bo‘lgandagi qoldiq bo‘lsin.
Agar Σ n=1^∞R n=-4/9 bo‘lsa, a ning qiymati nechaga teng?