广义P-级数的敛散性及其估值公式

The Convergence-Divergence and Estimation Formula of Generalized p-Series

讨论了广义p 级数的敛散性 ,给出部分和Sn 的估值公式 ,当数列 {Sn}收敛时 ,给出级数和的估值范围 ;当数列 {Sn}发散时 ,构造一类与之密切联系的收敛数列 {Yn} ;并且收敛数列 {Sn} (p>1 )与 {Yn} (0 <p<1 )

In the paper, we discuss the convergence and divergence of generalized p-series, give the estimation formula of partial sum Sn If sequence ｛S n｝is convergent ,the estimation range of series sum is geven; if sequence ｛S n｝is divergent,a class of convergent sequence ｛y n｝are proposed and convergent sequence ｛S n｝(p>1)are one -one correspondent with ｛y n｝(0<p<1)