Solve a mathematical factorial sequence sum: ∑ (cos3n) / N! N from 0 to infinity, thank you

Solve a mathematical factorial sequence sum: ∑ (cos3n) / N! N from 0 to infinity, thank you

The result is cos (SIN3) * e ^ (cos3)
The process is not very long, but it is troublesome to write! If you want the process, hi me!

Factorial and sequence problems
2/3!+3/4!+4/5!+.+99/100!
Where, the factorial is n * (n-1) * (n-2) *. * 2 * 1

2/3!+3/4!+4/5!+.+99/100!=(3-1)/3!+(4-1)/4!+(5-1)/5!+.+(100-1)/100!=1/2!+1/3!+1/4!+.+1/99!-(1/3!+1/4!+1/5!+.+1/100!)=1/2!-1/100!

2/(3!)+3/(4!)+4/(5!)+…… +99/(100!)

2/(3!)+3/(4!)+4/(5!)+…… +99/(100!) =(3-1)/(3!)+(4-1)/(4)+…… +(100-1)/(100!) =3/3!-1/3!+4/4!-1/4!+…… +100/100!-1/100!=3/3!+!+4/4!+…… +100/100!-(1/3!+1/4!+…… +1/100!)=0.5-1/100!

Can the reciprocal of rational number be irrational
A. Is the reciprocal of the mapping f: X -- X from a to B valid?

First of all, as long as the reciprocal of a rational number is meaningful, it must be rational, never irrational, but it may be meaningless, because 0 is rational, but the reciprocal of 0 is meaningless

If the reciprocal of rational number m is equal to itself, then CD is divided into m + (a + b) m - | M|=

Irrational numbers a and B are opposite to each other: a + B = 0
Irrational numbers C and D are reciprocal: C * d = 1
The reciprocal of rational number m is equal to itself: M = 1 / m, so m = 1 or M = - 1, | m | = 1
I don't understand what the molecule is, but it's easy to get the result by substituting

Let a be a rational number that is not equal to zero, and B be an irrational number. Then the following four numbers must be irrational numbers
A.a³+b³ B.（a+b)³ C.(a+b)b D.(a+b)a

C
B ^ 3 in a may be rational
In B: if a = 1, B = 3 ^ (1 / 3) - 1
Rational number multiplied by irrational number in D must be irrational number

Is there the smallest irrational number? Is there the smallest real number? Is there the smallest absolute number?

Is there the smallest irrational number? Is there the smallest real number? Is there the smallest absolute number?
Answer: there is no minimum irrational number and no minimum real number. The number with the minimum absolute value is 0

Real numbers are divided into positive real numbers? No? There is no real number with the largest absolute value. Is there the sum of the smallest two irrational numbers or irrational numbers?
Are all numbers with roots rational?

Real numbers are divided into positive real numbers, zero real numbers and negative real numbers. There is no real number with the largest absolute value, and the real number with the smallest absolute value is zero. The sum of two irrational numbers is not necessarily irrational. The irrational number does not necessarily have a root sign, and the irrational number can not be eliminated. There are many other irrational numbers

If a is the smallest positive integer, B is an irrational number, and C is the number with the smallest absolute value, find the product of the three numbers

A is the smallest positive integer, 1
C is the absolute value, and the smallest number is 0
The product of these three numbers ABC = 0

The absolute value of irrational number must be_______ .

The absolute value of irrational number must be positive