Question

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

Answer 1

The given expression is

`\sum ^8_(i\mathop=1)-(-2)^(i-1)`

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

`\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}`

Now, we sum all these items

`-1+2-4+8-16+32-64+128=85`

Therefore, the total sum is 85.