Question

D = 3^10 - 3^9 + 3^8 - 3^7 + ... + 3^2 - 3^1

Answer 1

\(3D=3^{11}-3^{10}+3^9-...+3^3-3^2\)

3D  + D = \(3^{11}-3^{10}+3^9-...+3^3-3^2+3^{10}-3^9+3^8-3^7+..+3^2-3^1\)

4D         \(=3^{11}-3\)

=> D = \(\frac{3^{11}-3}{4}\)

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Answer 2

D = 3¹⁰-3⁹+3⁸-3⁷+....+3²-3¹

3D = 3¹¹-3¹⁰+3⁹-3⁷+...+3³-3²

4D = 3D + D = 3¹¹-3¹

=> D = \(\frac{3^{11}-3}{4}\)