Question

Compute each sum below. If applicable, write your answer as a fraction.3 + 3(−3) + 3(−3)² + . . . + 3(-3)° = □Σ (3) - 0i = 1X

Answer 1

Part 1

we have the expression

`\begin{gathered} 3+3(-3)+3(-3)^2+3(-3)^3+3(-3)^4+3(-3)^5+3(-3)^6 \\ 3-9+27-81+243-729+2,187 \\ 1,641 \end{gathered}`

The answer Part 1 is 1,641

Part 2

we have the expression

`\begin{gathered} \sum_(i=1)^9((1)/(4))^i=(1)/(4)+(1)/(4^2)+(1)/(4^3)+(1)/(4^4)+(1)/(4^5)+(1)/(4^6)+(1)/(4^7)+(1)/(4^8)+(1)/(4^9) \\ \\ =(65,536+16,384+4,096+1,024+256+64+16+4+1)/(262,144) \\ \\ =(87,381)/(262,144) \end{gathered}`

The answer Part 2 is 87,381/262,144