give me more details about infinite series?

Answer 1

It's like the NHL, they try and they try but they cannot stop it from continuing

Answer 2

Infinite series that converge are very useful and can be used to obtain certain values to any degree of accuracy desired.

Some examples:
sin x = x- x^3/3! +x^5/5 - .... +(-1)^(n+1)[(x^(2n-1))/(2n-1)!] + .....
cosx = 1- x^2/2! + x^4/4! - ...+(-1)^(n+1)[(x^(2n-2))/(2n-2)!] + ...
e^x = 1+x +x^2/2!+x^3/3! +x^4/4! +.... x^n/n! + ......
pi/4 = 1-1/3+1/5-1/7+1/9- 1/11 +..........

The harmonic series 1+1/2 +1/3+1/4 +1/5 +...1/n ...
is divergent and if continued forever will grow infinitely large.

The geometric series 1+r+r^2 +r^3 +....r^n +.....
is convergent if |r|<1; otherwise it is divergent. If |r| < 1, the series will converge to the value 1/(1-r)

Answer 3

Series may be finite, or infinite; in the first case they may be handled with elementary algebra, but infinite series require tools from mathematical analysis if they are to be applied in anything more than a tentative way.

The sum of an infinite series a0 + a1 + a2 + ... is the limit of the sequence of partial sums

read more --> http://en.wikipedia.org/wiki/Series_(mathematics)

Answer 4

the series w/o the An th term is known as infinite series.

infinite series may or may not have a limit.

if it has the limit then the sum can be calculated by the formula:
s= a1/(1-r)

Answer 5

Learn to use a search engine. Then you can find thousands of websites about infinite series, convergence, divergence, and all manner of good stuff.


Doug