InterpolatingPolynomial[{4,5,2,1,5,2},x]
4+1+-2+1+-+(-4+x)(-3+x)(-2+x)(-1+x)
1
8
5-x
10
CoefficientList[Series[(1+x+x^2)/(1+x^3+3),{x,0,20}],x]
,,,-,-,-,,,,-,-,-,,,,-,-,-,,,
1
4
1
4
1
4
1
16
1
16
1
16
1
64
1
64
1
64
1
256
1
256
1
256
1
1024
1
1024
1
1024
1
4096
1
4096
1
4096
1
16384
1
16384
1
16384
ms3=MultiplicationTable[SymmetricPermutations[3]]
{{1,2,3,4,5,6},{2,1,5,6,3,4},{3,4,1,2,6,5},{4,3,6,5,1,2},{5,6,2,1,4,3},{6,5,4,3,2,1}}
ElementOrders[MultiplicationTable[SymmetricPermutations[3]]]
{1,2,2,3,3,2}
Tuples[{2,3},3]
{{2,2,2},{2,2,3},{2,3,2},{2,3,3},{3,2,2},{3,2,3},{3,3,2},{3,3,3}}
Table[Count[Fold[ms3[[#1,#2]]&,1,#]&/@Tuples[{2,3},i],1],{i,20}]
{0,2,0,6,0,22,0,86,0,342,0,1366,0,5462,0,21846,0,87382,0,349526}
Take[%,{2,-1,2}]
{2,6,22,86,342,1366,5462,21846,87382,349526}
Sum[((-2)^n/6+2^n/6+(-1)^n/3+1/3)x^n,{n,0,∞}]
1-3
2
x
(-1+x)(1+x)(-1+2x)(1+2x)
FullSimplify[%]
1-3
2
x
1-5+4
2
x
4
x
%127/RotateLeft[%127]//N
{0.333333,0.272727,0.255814,0.251462,0.250366,0.250092,0.250023,0.250006,0.250001,174763.}
1/%
{3.,3.66667,3.90909,3.97674,3.99415,3.99854,3.99963,3.99991,3.99998,5.72203×}
-6
10
Solve[1-5+40,x]
2
x
4
x
{x-1},x-,x,{x1}
1
2
1
2
Recognize[.24234234,4,x]
180-786x-23+596+971
2
x
3
x
4
x