infinite series formula

Let us learn about infinite series formula

Infinite Series Formula:
If -1<>2 + ar³ + ...... = a/ (1 - r)
Exponential series:
1. e^x = 1 + x + x²/ 2! + x³/ 3! + .....
2. e^-x = 1 - x + x²/ 2! - x³/3! + .......
3. 1/2 (e^x + e^-x) = 1 + x²/ 2! + x⁴/ 4! + .......
4. 1/2 (e^x - e^-x) = x/ 1! + x³/ 3! + x⁵/ 5! + .......
5. a^x = e^{x log}_e^a = 1 + x log_ea + (x log_ea)²/ 2! + (x log _ea)³/ 3! + ....... for a>0
these are the fomula in Infinite series formula applicable for exponential series.

Some more Formulas Infinite Series Formula:

log series:
1. log_e(1 + x) = x - x²/ 2 + x³/ 3 - x⁴/ 4 +.... for -1<>
2. log_e(1 - x) = -x - x²/ 2 - x³/ 3 - x⁴/ 4 -..... for -1<= x <1
3. log_e[(1 + x)/ (1 - x)] = 2[x + x³/ 3 + x⁵/ 5 +......] for -1<>
5. log_e2 = 1 - 1/2 + 1/3 - 1/4 + .....
In our next blog we shall learn about direction of magnetic field I hope the above explanation was useful.Keep reading and leave your comments.