Help understanding alternating infinite series?

[isukatphysics69]

Homework Statement

Homework Equations

The Attempt at a Solution

So my understanding of this so far is that the whole infinite series from 1 to infinities summation minus the first six terms summation is equal to 0.0002..? This is so confusing. So how does that mean that the sum will lie between that range at the bottom...What on earth

 

[mathwonk]

i recommend reading the chapter of courant's calculus book vol 1, on infinite series for this topic as well as a great treatment of convergence tests for series of constants.