Decomposition principle in summation

Provided we know how to sum the building blocks such as \(\sum_{r=1}^{n} 1\), \(\sum_{r=1}^{n} r\) and \(\sum_{r=1}^{n} r^2\), we will know how to simplify the final answer. For the purpose of evaluating summations, we now “airdrop” some standard formulae for these atomic building blocks which are within the scope of the IB HL Mathematics syllabus.