Question

Use summation notation to write the series -1+2-4+8-16... for 12 terms

Answer 1

The first 12 terms of the series are represented by:

`f(12) = \Sigma\limits_(i = 1)^(12) [(-1)^(n)\cdot 2^(n-1)] = -1 + 2 - 4 + 8 - 16 + 32 - 64 + 128 -256 + 512 - 1024 + 2048`

Explanation:

The summation notation for the series
`-1 + 2 -4 + 8 -16...` is represented by the expression
`f(n) = \Sigma\limits_(i = 1)^(n) [(-1)^(n) \cdot 2^(n-1)]`.

The first 12 terms of the series are represented by:

`f(12) = \Sigma\limits_(i = 1)^(12) [(-1)^(n)\cdot 2^(n-1)] = -1 + 2 - 4 + 8 - 16 + 32 - 64 + 128 -256 + 512 - 1024 + 2048`