Proof Without Words: Sums of Powers of

Abstract

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“…Therefore, we answer negatively the question raised by Edgar [1] on whether there are more similar "proofs without words" for other series.…”

“…The two ways must give the same answer, so we have the desired identity. Continuing the work, in 2016, Edgar [1] proved that 4 9 + ( 4 9 ) 2 + ( 4 9 ) 3 + • • • = 4 5 using Mabry's technique (see Figure 3). At the end of his proof, Edgar asked: "Is it possible to determine which other series allow ananalogous proof without words?".…”

“…We now apply (2.2) to have the two identities proven by Edgar [1] and Mabry [2]. In Mabry's proof, we have (n, a, r) = (3, 1, 1/2).…”