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Sa se calculeze 2S+1, unde S=3+3^2+3^3+...+3^99.

Răspuns :

S=3+3^2+3^3+...+3^99                    inmultim cu 3
3S
=3^2+3^3+...+3^99+3^100
3S-S=3^2+3^3+...+3^99+3^100-(3+3^2+3^3+...+3^99 )
2S=3^2+3^3+...+3^99+3^100-3-3^2-3^3+...-3^99
2S=3^100-3
2S-1=3^100-3-1
2S-1=3^100-4