(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

I want to show/prove that

√(y)√(1+y) - ln[√(y)+√(1+y)] = 2y^(3/2)/3 when y<<1 by series expansion.

2. Relevant equations

√(1+y) = 1+y/2 - (y^2)/8 + ....

and

ln[√(y)+√(1+y)] = ln[1 + √(y) + y/2 -(y^2)/8 + ....]

3. The attempt at a solution

I'm thinking I sub in the expansions above into the initial equation. My question then, is what do I do next?

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Series expansion

**Physics Forums | Science Articles, Homework Help, Discussion**