Home/Algebra/Sequences, finite series, and recurrences/Linearity of summation14. Sequences, finite series, and recurrencesLinearity of summationLevel: intermedioIn 14. Sequences, finite series, and recurrencesFormulaCopy LaTeX∑(ak+bk)=∑ak+∑bk;∑cak=c∑ak\sum(a_k+b_k)=\sum a_k+\sum b_k;\quad \sum ca_k=c\sum a_k∑(ak+bk)=∑ak+∑bk;∑cak=c∑akTagsalgebraalgebra formulasequencessequences series finitasDetailFundamental rules of sigma notation.Found an error? Contact us.Related formulasRelatedBinomial theorem(a+b)n=∑k=0n(nk)an−kbk(a+b)^n=\sum_{k=0}^{n}\binom nk a^{n-k}b^k(a+b)n=k=0∑n(kn)an−kbkOpen formulaOpen in section