<prompt> Hlalosa ho kopana ha tatellanonan  <response>: Instruction in English: Explain the convergence of a sequence . Response in English: Convergence of a sequence refers to the idea that as the sequence progresses, the terms get closer and closer to a specific value. This value is called the limit of the sequence. In other words, a sequence is said to converge if its terms approach a finite value as the sequence progresses towards infinity.To say that a sequence of numbers xn converges to a limit L, means that the difference between xn and L, i.e. xn - L, becomes smaller and smaller as n increases. In mathematical notation, we can write this formally as:limn- xn LThis means that for any given positive tolerance ε, there exists a positive integer N such that for all nN, the value of xn - L ε. This means that all terms of the sequence beyond the Nth term are within ε distance of the limit L.As an example, consider the sequence 12, 14, 18, ... in which each term is half of the previous term. This sequence converges to 0, since as n increases, each term gets closer and closer to 0.In contrast, a sequence that does not converge is referred to as a divergent sequence. An example of this would be the sequence 1,2, 3, ... which does not approach any specific value as n increases. . Response in Sesotho: Ho kopana ha tatelano ho bolela mohopolo wa hore ha tatelano e ntse e tswela pele, mareo a ntse a atamela ho feta boleng bo itseng. Boleng bona bo bitsoa moeli oa tatellano. Ka mantsoe a mang, ho boleloa hore tatellano ea kopana haeba mantsoe a eona a atamela boleng bo lekanyelitsoeng ha tatellano e ntse e tsoela pele ho ea ho se nang moeli. Ho bolela hore tatellano ea linomoro xn e fetoha moeli oa L, ho bolela hore phapang pakeng tsa xn le L, ke hore xn - L, e fetoha e nyenyane le e nyenyane ha n e ntse e eketseha. Lintlheng tsa lipalo, re ka ngola sena ka mokhoa o hlophisitsoeng joalo ka: limn- xn L Sena se bolela hore bakeng sa mamello efe kapa efe e fanoeng ε, ho na le palo e kholo ea N hoo ho bohle nN, boleng ba xn - L ε. Sena se bolela hore lipehelo tsohle tsa tatellano ho feta nako ea Nth li ka hara ε sebaka sa moeli oa L. E le mohlala, nahana ka tatellano 12, 14, 18, ... eo ho eona nako ka ngoe e leng teng. halofo ea nako e fetileng. Tatelano ena e kopana ho 0, kaha ha n e ntse e eketseha, lereo le leng le le leng le ntse le atamela le ho atamela ho 0. Ka lehlakoreng le leng, tatelano e sa kopane e bitsoa tatelano e fapaneng. Mohlala oa sena e ka ba tatellano 1,2, 3, ... e sa atameleng boleng leha e le bofe bo khethehileng ha n e ntse e eketseha. 