Partial Sums Multiplying to a Power of Two
Difficulty: Hard · Topics: Calculus, Series, Sequences
Ko‘paytmasi ikkining darajasi bo‘lgan qismiy yig‘indilar
Let S n be the sum of the first n terms of the sequence \a n\, where
a 1=4, S nS n+1=2^n (n=1,\ 2,\ 3,\ …).
Find the value of lim n→∞≤ft(frac15a 2na 2n-1+frac8S 2nS 2n-1 ).
S n — \a n\ ketma-ketlikning birinchi n ta hadi yig‘indisi, bunda
a 1=4, S nS n+1=2^n (n=1,\ 2,\ 3,\ …).
lim n→∞≤ft(frac15a 2na 2n-1+frac8S 2nS 2n-1 ) ning qiymatini toping.