设数列{Un}收敛,则n→∞时limUn=limUn+k是否成立RT

设数列{Un}收敛,则n→∞时limUn=limUn+k是否成立RT
设数列{Un}收敛,则n→∞时limUn=limUn+k是否成立
RT

设数列{Un}收敛,则n→∞时limUn=limUn+k是否成立RT
设数列收敛于t
那么有lim[n -> ∞] U[n] = t
且lim[n -> ∞] U[n+k] = lim[(n+k) -> ∞] U[n+k] = t
所以n -> ∞时,lim U[n] = lim U[n+k]