ums and Approximations 2 Sums of powers Pharaoh Aha I decides to build a"pyramid "in his own honor consisting of a single block His successor, Aha Il, trumps him by building a larger pyramid Not to be outdone, Aha Ill builds a still-larger pyramid If this madness continues, how many blocks will Pharoah Aha n require? Lets break the problem down by chopping the n-th pyramid into n horizontal slabs Therefore, we have # blocks in n-th pyramid=># blocks in k-th slab Similarly, we can slice each slab into columns� 6 Sums and Approximations 2 Sums of Powers Pharaoh Aha I decides to build a “pyramid” in his own honor consisting of a single block: His successor, Aha II, trumps him by building a larger pyramid: Not to be outdone, Aha III builds a still­larger pyramid: If this madness continues, how many blocks will Pharoah Aha n require? Let’s break the problem down by chopping the n­th pyramid into n horizontal slabs: Etc. Therefore, we have: n # blocks in n­th pyramid = # blocks in k­th slab k=1 Similarly, we can slice each slab into columns: