Adding Powers of 9

90+91=1+9=1091+92=9+81=9092+93=81+729=810\begin{array}{rcccr} {\color{#D61F06}9^0}+9^1 & = & {\color{#D61F06}1}+9 & = & {\color{#D61F06}1}0 \\ {\color{#D61F06}9^1}+9^2 & = & {\color{#D61F06}9}+81 & = & {\color{#D61F06}9}0 \\ {\color{#D61F06}9^2}+9^3 & = & {\color{#D61F06}81}+729 & = & {\color{#D61F06}81}0 \\ \end{array}

Is the following true for any positive integer n?n? 9n+9n+1=9n×10{\color{#D61F06}9^n}+9^{n+1}={\color{#D61F06}9^n} \times 10

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