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T. Series
Taylor series and their summation equivalents
| Question | Answer |
|---|---|
| 1/(1-x) | sum k=0 to infinity x^k ; |x|<1 |
| 1/(1+x) | sum k=0 to infinity (-1)^k x^k ; |x|<1 |
| e^x | sum k=0 to infinity (x^k)/k! ; |x|<infinity |
| sin(x) | sum k=0 to infinity [(-1)^k x^(2k+1)]/[(2k+1)!] ; |x|<infinity |
| cos(x) | sum k=0 to infinity [(-1)^k x^(2k)]/[(2k)!] ; |x|<infinity |
| ln(1+x) | sum k=1 to infinity [(-1)^(k+1) x^k]/k ; -1<x<1 |
| -ln(1-x) | sum k=1 to infinity (x^k)/k ; -1<x<1 |
| arctan(x) | sum k=0 to infinity [(-1)^k x^(2k+1)]/(2k+1) ; |x|<1 |
| (1+x)^p | sum k=0 to infinity (p k)x^k |x|<1 where (p k) = [p(p-1)(p-2)...(p-k-1)/k!] and (p 0) = 1 |
Created by:
courtneyllyons
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