When Two Limits Agree
Difficulty: Medium · Topics: Calculus, Limits, Sequences
Ikki limit teng bo‘lganda
For
lim n→∞frac3n^k-1(n^2+1)(n^3-1)=α, lim n→∞fracn(n+5)3n^k-1=β,
how many natural numbers k satisfy α=β? (Here α and β are constants.)
lim n→∞frac3n^k-1(n^2+1)(n^3-1)=α, lim n→∞fracn(n+5)3n^k-1=β
bo‘lsa, nechta natural k son α=β ni qanoatlantiradi? (Bu yerda α va β — o‘zgarmaslar.)