Question

Express the series using sigma notation 5 -10 + 20 - 40 + 80 - ...

Answer 1

`\displaystyle \text{series}=\sum_(n=0)^(\infty){5\cdot(-2)^n}`

Explanation:

The first term is 5 and the common ratio is -2. The general term for n starting at 1 can be written as ...

an = a1·r^(n-1)

If we start n at 0, then we can eliminate the -1 from the exponent:

`\displaystyle \text{series}=\sum_(n=0)^(\infty){5\cdot(-2)^n}`