Determine the sum of each geometric series.
[tex]\begin{gathered} \sum ^5_{k\mathop=1}3(2)^{k-1}=3\cdot(2)^0+3\cdot(2)^1+3\cdot(2)^2+3\cdot(2)^3+3\cdot(2)^4 \\ =3+6+12+24+48 \\ =93 \end{gathered}[/tex][tex]\begin{gathered} \sum ^5_{k\mathop=1}3^{k-1}=3^0+3^1+3^2+3^3+3^4 \\ =1+3+9+27+81 \\ =121 \end{gathered}[/tex][tex]\begin{gathered} \sum ^7_{k\mathop=1}2^{k-1}=2^0+2^1+2^2+2^3+2^4+2^5+2^6 \\ =1+2+4+8+16+32+64 \\ =127 \end{gathered}[/tex][tex]\begin{gathered} \sum ^4_{k\mathop=1}2\cdot(3)^{k-1}=2\cdot(3)^0+2\cdot(3)^1+2\cdot(3)^2+2\cdot(3)^3 \\ =2+6+18+54 \\ =80 \end{gathered}[/tex]Thus sums can be arranges from smallest to largest as,
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