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Question
Write the first 6 terms of the exponential series
`"e"^(-2x)`
Solution
ex = `1 + x/(∠1) + x^2/(∠2) + x^3/(∠3)`
`"e"^(-2x) = 1+ (-2x)/(∠1) + (-2x)^2/(∠2) + (-2x)^3/(∠3) - ...`
= `1 - 2x + (4x^2)/2 - (8x^2)/6 + (16x^4)/24 - (32x^5)/120 + (64x^6)/45 - ...`
= `1 - 2x + 2x^2 - (4x^3)/3 + (2x^4)/3 - (4x^5)/15 + (4x^6)/45 - ...`
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