Question

Consider the geometric series, ln x + p ln x + 1/3 in x + ... Where x is a real number, x>1 and p is a real number that is not 0. Prove that p= positive or negative 1/square root of 3.

Answer 1

HI,

Explanation:

The series is the sum of the terms of the sequence:

`u, u*r,u*r^2,r*u*r^3,...,u*r^n,...\\u\ is\ the\ first\ term\\and \ r\ the \ ration.\\\\Here\ p=r \ and\ r^2=(1)/(3) \\\\r=\sqrt{(1)/(3) } =(1)/(√(3) ) \\\\u=ln(x)\\\\`