Question

A function f (θ) is defined as:
f(θ)= 1 - θ + θ^2/2! - θ^3/3! + θ^4/4! ....
Why is it necessary for q to be a dimensionless quantity?

Answer 1

f(θ) =  1 - θ + θ^2 / 2!  -  θ^3 / 3!  + θ^4 / 4!  .....
       = e^{-θ}

   θ has to be a dimensionless quantity as the exponent in a power ha to be a number only...

   θ has to be a dimensionless quantity as the various terms in the express on RHS have different powers of  θ..  So if θ has dimensions, then the terms on RHS cannot be added.