Exponential series question

(a) Show that for any positive integer n greater than 2, 1/n! < 1/2n-1
1 < (2/2)(3/2)(4/2)...(n/2)
1 < n! / 2n-1
1 / n! < 1 / 2n-1
(b) using the exponential series, show that e = 1+1+1/2!+.......
ex = 1 + x + x2/2! + x3/3! + ...
Sub x = 1, e = 1 + 1 + 1/2! + 1/3! + ...
(c) Hence deduce that e<3
Use the result in (a)
e = 1 + 1 + 1/2! + 1/3! + ... < 1 + (1 + 1/2 + 1/4 + ...)
= 1 + 1/(1 - 1/2)
= 1 + 2
= 3
So e < 3
The curve y =A + B(3cx) as shown cuts y-axis at the point P(0,3) and is getting very near to the line y=1 as x becomes large
(a) Find the values of A and B
Sub P into y = A + B(3cx)
3 = A + B
When x is large, if c is positive, 3cx approaches infinity. If c is negative, 3cx approaches 0.
The former case cannot make y approaches 1 so c is negative.
1 = A
and B = 2
(b) If the curve also passes through the point (1,5/3), find the c.
The question may have a mistake, I changed 3/5 to 5/3.
y = 1 + 2(3cx)
5/3 = 1 + 2(3c)
2/3 = 2(3c)
3c = 1/3
c = -1