Recovering a Sequence from Its Sums
Difficulty: Medium · Topics: Algebra, Sequences, Telescoping
Ketma-ketlikni yig‘indilaridan tiklash
The sequence \a n\ satisfies the following for all natural numbers:
Σ k=1^n(1)/((2k+1)a k)=n^2.
When Σ k=1^12a k=p/q, find p+q. (p and q are coprime)
\a n\ ketma-ketlik barcha natural sonlar uchun quyidagini qanoatlantiradi:
Σ k=1^n(1)/((2k+1)a k)=n^2.
Σ k=1^12a k=p/q bo‘lganda p+q ni toping. (p va q o‘zaro tub)