Calculate Cn and Sn?

Cn=cosh(kx)
Sn=sinh(kx)

where k=1 and n is an element of N*

1 Answer

See below.

Explanation:

Cn=nk=0cosh(kx)=12nk=0ekx+12nk=0ekx

but, using the formula for the sum of geometric sequences,

nk=0ekx=e(n+1)x1ex1

nk=0ekx=e(n+1)x1ex1

and

Cn=12(e(n+1)x1ex1+e(n+1)x1ex1)=12(1+cosh(nx)+coth(x2)sinh(nx))

with similar procedure we get at

Sn=12(e(n+1)x1ex1e(n+1)x1ex1)=csch(x2)sinh(nx2)sinh(12(1+n)x)