Question

Arrange the geometric series from least to greatest based on the value of their sums. 5 5 ΣΠ2) 4-1 Σ3-1 Σ 26-1 Σ2(3):-1! =1 < Λ

Answer 1

Determine the sum of each geometric series.

`\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}`
`\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}`
`\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}`
`\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}`

Thus sums can be arranges from smallest to largest as,