Question

Arrange the summation expressions in order from least to greatest according to the value of each sum

Answer 1

- Let us evaluate the summations given to us and we can thus know the order.

`\begin{gathered} \sum ^5_(k=1)4(2)^(k-1)=4(2)^0+4(2)^1+4(2)^2+4(2)^3+4(2)^4 \\ \\ \sum ^5_(k=1)4(2)^(k-1)=4+8+16+32+64=124 \end{gathered}`

`\begin{gathered} \sum ^4_(k=1)3(4)^(k-1)=3(4)^0+3(4)^1+3(4)^2+3(4)^3 \\ \\ \sum ^4_(k=1)3(4)^(k-1)=3+12+48+192=255 \end{gathered}`

`\sum ^3_(k=1)6^(k-1)=6^0+6^1+6^2=1+6+36=43`

`\begin{gathered} \sum ^2_(k=1)2(5)^(k-1)=2(5)^0+2(5)^1 \\ \\ \sum ^2_(k=1)2(5)^(k-1)=2+10=12 \end{gathered}`

- Therefore, we can order the sums