> evalf(1-1/2);

> evalf(1-1/2+1/3);

> evalf(1-1/2+1/3-1/4);

> evalf(1-1/2+1/3-1/4+1/5);

> evalf(1-1/2+1/3-1/4+1/5-1/6);

So the first several terms of the alternating harmonic series are:

1, .5, .833..., .5833..., .7833..., .6166..., ....

Based on what's happened so far, what do you think the 7th partial sum of this alternating series will be, roughly?

> f := n -> sum((-1)^(k+1)/k, k=1..n);

> evalf(f(10));

> evalf(f(100));

> evalf(f(1000));

> evalf(f(2000));

> evalf(f(5000));

> evalf(f(6000));

>