Let R be the subring {x + yi : x, y in 2Z} of C, and
let I be the ideal {x + yi : x,y in 2Z}of R.
How many additive cosets has I in R? List them clearly.
I know definition of ideal but ı don't know how to write in set is that question describe.Please help :)
Find an approximate value of the number e-0.1 with an error less than 10-3
ı know that ex = Ʃ(from zero to ınfinity) xn / n!=1+x/1!+x
2/2!+...
ı don't know how to use e-0.1 in this question.Do ı write -0.1 instead of x in ex series?
Ʃ (from n=1 to ınfınıty ) n /(n+1)!
the questions asks sum of the this series.
I try to write this series as Ʃ 1/(n-1)!.(n+1)but ı couldn't simulate any series.
How can ı do this ?
H=A3= {(1),(1 2 3),(1 3 2)} and
G=S3 ={ (1),(1 2 3),(1 3 2),(1 2 ),(1 3),(1 2 3) }
Is H is normal subgroup of G ?
I try g=(1 2 3 ) for gH=Hg but gH≠Hg for all g ε G.In this situation,H is normal subgroup pf G?
The question wants all subgroups of S3 . If H≤S 3 , then ; IHI=1,2,3,6 by Lagrance's Theorem.
In other words, order of H can be 1,2,3 and 6.
What ı want to ask is how to write subgroup of S3. For example,is H 1 (1) ?
A sequence (an) is recursively defined by a1 = 1 and
an+1 =1 /(2+an ) for all n≥1
I'll prove this sequence is convergent by monoton sequence theorem.ı can find ıt is bounded but ı cannot decide it is monoton because when ı write its terms,Its terms are increasing sometimes decreasing...
an = [cos (3n) )] /n.cos(1/n) My solution is , I wrote an as
liman→∞ [cos (3n) )] /[ cos(1/n) / (1/n) ) .
We get liman→∞ cos(3n) / ( 1/0 ) .
I think solution of this limit is zero but ı'm not sure cos(3n) .I think cos(3n) as a number and number/infinity is zero .As a result of...
If the circumference of the region bounded by the curve y=cosh(x) and the lines y=0 x=a
and x=-a is 2a+4, where a>0 find the area of the surface obtained by rotating the part of
the curve y=cosh(x) between x=a x=-a and around the x axis. This is my homework question.I tried to solve it.I...
My sequence is the second one.If it is neither increasing or decreasing ,how will ı show that it is convergent sequence? ı think there is a problem about sequence.
Thank you for efforts :)