common taylor series for calc final

1/(1-x)

sum from 0 to infin of xⁿ

converges for 1/(1-x)

converges for abs value of x < 1

ln (1+x)

sum from 0 to infin of (-1)ⁿ (xⁿ⁺¹) / (n+1)

convergence for ln (1+x)

converges for abs value of x < 1

e^x

sum from zero to infin of (xⁿ) / (n!)conv

convergence for e^x

converges for all x

sin x

sum from zero to infin of (-1)ⁿ (x²ⁿ⁺¹) / (2n+1)!

convergence for sin x

converges for all x

cos x

sum from 0 to infin of (-1)ⁿ (x²ⁿ) / (2n)!

convergence for cos x

converges for all x