"Little o" function Claim: et= 1 + t +o(t) Proof: et = 1 + t + t2/2! + t3/3! +... Let g(t)=t2/2! + t3/3! +... g(t) is o(t), thus et= 1 + t +o(t). ================= I don't understand why g(t) is o(t). Why is it true that lim g(t)/t = 0 ? t->0 I know that for example lim[f(x)+g(x)]=lim f(x) + lim g(x), so if lim f(x)=0 and lim g(x)=0, then lim[f(x)+g(x)] = 0+0 = 0. I believe this property is true only when computing the limit of a sum of a FINITE number of functions. But g(t)/t above is an infinite sum; it has an infinite number of terms. How can we compute and prove that the limit of g(t)/t is 0? I know each term goes to 0, but we are summing an INFINITE number of terms, so how can you be sure that the limit is 0? Any help/explanations would be much apprecaited!