If `n` is any positive integer, write the value of `(i^(4n+1)-i^(4n-1))/2` .

Explanation

`frac{i^{4 n+1}-i^{4 n-1}}{2}`

`=frac{i-frac{1}{i}}{2}( i^{4 n}=1, i^{-1}=frac{1}{i})`

`=frac{frac{i^{2}-1}{i}}{2}`

`=frac{i^{2}-1}{2 i}`

`=frac{-1-1}{2 i}`

`=frac{-2}{-2 i}`

`=frac{-1}{i}`

`=frac{-i}{i^{2}}( i^{2}=-1)`

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