Given S=1+2 negative first power +2 negative second power +2 negative third power +…… +2 Negative 2012.

S=1+2^-1+2^-2+2^-3+...+2^-2011+2^-2012
2S=2+1+2^-1+2^-2+2^-3+...+2^-2011
2S-S=2-2^-2012
S=2-2^-2012

S=1+2 negative first power +2 negative second power +2 negative third power +…… +2 Minus 2010 power

Multiply both sides by 2
2S=2+1+2 negative first power +2 negative second power +2 negative third power +…… +2 Minus 2009 power
S=1+2 negative first power +2 negative second power +2 negative third power +…… +2 Minus 2009 power +2 minus 2010 power
S=2-2 minus 2010 power

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