Answered

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8Σ-(-2): -1-i=1Evaluate each geometric series described. (Find the total sum)

Sagot :

The given expression is

[tex]\sum ^8_{i\mathop=1}-(-2)^{i-1}[/tex]

To solve this, we just have to replace each value of the sum in the expression, then we sum. Let's do it

[tex]\begin{gathered} -(-2)^{1-1}=-1 \\ -(-2)^{2-1}=-(-2)^1=2 \\ -(-2)^{3-1}=-(-2)^2=-4 \\ -(-2)^{4-1}=-(-2)^3=8 \\ -(-2)^{5-1}=-(-2)^4=-16 \\ -(-2)^{6-1}=-(-2)^5=-(-32)=32 \\ -(-2)^{7-1}=-(-2)^6=-64 \\ -(-2)^{8-1}=-(-2)^7=-(-128)=128 \end{gathered}[/tex]

Now, we sum all these items

[tex]-1+2-4+8-16+32-64+128=85[/tex]

Therefore, the total sum is 85.

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