The paper deals with the space of linear recurrent sequences, i.e., the complex vector space generated by all the sequences \(s_{a,k}(m) = {m \choose k}a^{m-k}\), for \(a\) a complex number and \(k\) a natural number. The author studies sections and sums of linear recurrent sequences. A section of a sequence \(F(k)\) is a sequence \(G(k) = F(rk+s),\) where \(r\) and \(s\) are fixed integers. The sum of \(F(k)\) is the sequence \(\sum F(m) = \sum_{k=0}^{m-1} F(k),\) and a lacunary sum of \(F\) is the sum of a section of \(F.\) General formulas and recurrence relations for several types of sums of binomial coefficients are given.