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Question Number 56597 by Tawa1 last updated on 19/Mar/19

Commented by Tawa1 last updated on 19/Mar/19

$$\mathrm{Please}\mathrm{help}\mathrm{me}\mathrm{prove}\mathrm{the}\mathrm{sum}\mathrm{of}\mathrm{an}\mathrm{arithmetico}-\mathrm{geometric}\mathrm{series},$$$$\mathrm{and}\mathrm{the}\mathrm{sum}\mathrm{to}\mathrm{infinity}.$$$$\mathbf{Again}$$$$\mathrm{How}\mathrm{does}\mathrm{the}3\mathrm{x}\mathrm{in}\mathrm{the}\mathrm{above}\mathrm{solution}\mathrm{disappear}.$$$$\mathrm{From}3\mathrm{x}+({2\mathrm{x}}^2+{2\mathrm{x}}^3+...+{2\mathrm{x}}^{\mathrm{n}})-(2\mathrm{n}+1){\mathrm{x}}^{\mathrm{n}+1}$$$$\mathrm{to}\mathrm{x}+(2\mathrm{x}+{2\mathrm{x}}^2+{2\mathrm{x}}^3+...+{2\mathrm{x}}^{\mathrm{n}})-(2\mathrm{n}+1){\mathrm{x}}^{\mathrm{n}+1}$$$$\mathrm{in}\mathrm{next}\mathrm{line}...$$$$$$$$\mathrm{Thanks}.$$

Commented by Kunal12588 last updated on 19/Mar/19

$$3x+(2x^2+2x^3+...+2x^n)-..$$$$=x+2x+(2x^2+2x^3+...+2x^n)-...$$$$=x+(2x+2x^2+2x^3+...+2x^n)-...$$

Commented by Tawa1 last updated on 19/Mar/19

$$\mathrm{Ohh}.\mathrm{I}\mathrm{understand}\mathrm{now}.\mathrm{God}\mathrm{bless}\mathrm{you}\mathrm{sir}...$$

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