2^13+2^12+2^11+2^10+2^9+2^8+2^7+2^6+2^5+2^4+2^3+2^2+2+1

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S = 2^0+2^1+...+2^13 (1)
2S= 2^1+2^2+...+2^14 (2)
(2)-(1)
S = 2^14 -1
2^0+2^1+...+2^13 =S=2^14 -1

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1=2-1
1+2=2^2-1
2^2+2+1=2^3-1
...
=2^14-1

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