Question

what is meant by convergence of a sequence in simple terms

Answer 1

it means the sequence has a finite answer.
if I try to find the sum of 1+2+3+4+.................., i never get a finite answer. so this sequence is said to be divergent.

Answer 2

http://en.wikipedia.org/wiki/Convergent_series#Examples_of_convergent_and_divergent_series

Answer 3

you sound absolutely right!good link too.nways whats a power series??

Answer 4

Power series: infinite series of the form a1+a2(x-b)+a3(x-b)^2+a4(x-b)^3+...

Answer 5

ask more :)

Answer 6

u studying what??

Answer 7

no not these type of questions..ask me math problems...:)

Answer 8

dhatraditya defined convergence for series..u wanted convergence in of sequence...

Answer 9

whats the difference between series and sequence??arent they same ??

Answer 10

no..thats a conceptual error.
SEQUENCE:ordered list of objects (or events). Like a set, it contains members (also called elements or terms), and the number of terms (possibly infinite) is called the length of the sequence. Unlike a set, order matters, and exactly the same elements can appear multiple times at different positions in the sequence. A sequence is a discrete function.
SERIES:sum of terms of a sequence

Answer 11

well defined!so whats d convergence of sequence??

Answer 12

first u need to know the definition of limit of a sequence: The limit of a sequence (xn) is, intuitively, the unique number or point L (if it exists) such that the terms of the sequence become arbitrarily close to L for "large" values of n. If the limit exists, then we say that the sequence is convergent and that it converges to L.

Answer 13

ask more...:)

Answer 14

u seem to have a voracious hunger for questions :)whats a homogenous linear equation??

Answer 15

a system of linear equation is homogeneous if the constant terms vanish i.e. are 0. for eg.

x+y=0 and
2x+3y=0

Answer 16

ask more? (plz make sure u understand)

Answer 17

do u want to learn all about sequence,series and convergence, divergence? I can make a pdf for u if u want..u can gimme ur email id...

Answer 18

presently having problem with my id.nyways will definetly give u soon.learnt a lot today!nways what is an invertible function and how to identify it??

Answer 19

invertible functions are functions having inverses. bijective functions are invertible.

Answer 20

please elaborate if possible

Answer 21

ok..wat do u know of inverse function?....or can u define a function?...wat exactly is a function? i will proceed after u tell.

Answer 22

by function i can understand that it relates on two dependent and an independent variable.eg.f(x)=y here value of y is dependent on value of x(independent variable).a variable can be dependent on two indepent variable too or more.

Answer 23

I start from the basics:
FUNCTION:A function assigns to each element of a set say A, a unique element of another set say B.
Here A is called the domain and B is called the range of the function.

Do u know what is bijection?

Answer 24

i know.for every elment in set b there is exactly one element in a with which it relates.can be onto or or one one.no element remains to be mapped in set a or b.

Answer 25

good..thats it! a bijection is always invertible

Answer 26

so in inversion of function the the domain is represented in the function of its range!hope i be true!

Answer 27

I couldnt understand u! :(

INVERSE FUNCTION: if ƒ is a function from a set A to a set B, then the inverse of ƒ is a function from B to A, with the property that a round trip from A to B to A (via a composition of ƒ and its inverse) returns each element of A to itself. Thus, if an input x into the function ƒ produces an output y, then inputting y into the inverse function produces the output x, and vice versa.
suppose g is inverse of f.
If ƒ maps X to Y, then g maps Y back to X.
So we get g(f(x))=x for all x in domain of f.

Answer 28

thanks!very elaborate.how can a complex function be plotted ??

Answer 29

u cant plot in usual graphs but need the complex plane..

Answer 30

you "map" , a region from one plane ( z plane ) to another plane called the w plane (usually )

Answer 31

a graph of a function of a complex variable needs 4 dimensions , it requires 4 mutually perpendicular axes , which is not possible since we live in three dimension

Answer 32

cannot the x axis denote the real part nd y axis as imaginary part??

Answer 33

2 axes to represent the real and imaginary parts of the inputs, and another two axes to represent the real and imaginary parts of the output

Answer 34

hows network analysis @elecengineer??