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

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

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