# calculus – Prove that such number \$C\$ exists..

The task is to prove that for sequences $${ a_n }$$ and $${ A_n }$$ for which the following is right: $$a_n-(A_n-A_{n-1})=c_n$$, where series $$sum c_n$$ is converging do exist such number $$C$$, that $$a_1+a_2+a_3+…+a_n=A_n+C+O(1)$$ (O(1) – O-notation here).

Came across this one during my prepartion for an exam I’m taking in a week. May you help with this one?