$$2^0+2^1+2^2+2^3+\dots+2^n = 2^{(n+1)} - 1$$
I want to know is there a simple (visual/intuitive/elementary) explanation for this. How can I explain the reason behind this result to a layman?
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Would something along the lines of starting with $2^{n+1}$ objects and repeated taking away half of the remainder work? – Michael Burr Jan 02 '22 at 12:47
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1$2\times S=S+2^{n+1}-1$, by inspection. – lulu Jan 02 '22 at 12:47