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Question
Write the first 6 terms of the exponential series
e5x
Solution
ex = `1 + x/(∠1) + x^2/(∠2) + x^3/(∠3)`
So e5x = `1 (5x)/(∠1) + (5x)^2/(∠2) + (5x)^3/(∠3) + (5x)^4/(∠4) + ....`
= `1 + 5x + (25x^2)/2 + (125x^3)/6 + (625x^4)/24 + 3125/120 x^5 + 15625/72 x^6 ...`
= `1 + 5x + (25x^2)/2 + (125x^3)/6 + (625x^4)/24 + (625x^5)/24 + (3125x^6)/144 ...`
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