I NEED HELP WITH SERIES PROBLEM..

$$\sum_{n=1}^{\infty} \frac{ (-1)^\left( n+1 \right) }{ 2^n+n }$$

(a) estimate the series
by evaluating $$S_2$$
i put n=1,2 so S_2
$$\frac{ 1 }{ 3 }-\frac{ 1 }{ 5 }=\frac{ 2 }{ 15 }=S_2$$ (is this correct?)

(b) determine the error bound for
$$\left| S_3-\sum_{n=1}^{\infty} \frac{ (-1)^\left( n \right) }{ 2^n+n } \right|$$

Question

I NEED HELP WITH SERIES PROBLEM..

$$\sum_{n=1}^{\infty} \frac{ (-1)^\left( n+1 \right) }{ 2^n+n }$$

(a) estimate the series 
by evaluating $$S_2$$
      i put n=1,2 so S_2 
$$\frac{ 1 }{ 3 }-\frac{ 1 }{ 5 }=\frac{ 2 }{ 15 }=S_2$$          (is this correct?)

(b) determine the error bound for 
$$\left| S_3-\sum_{n=1}^{\infty} \frac{ (-1)^\left( n \right) }{ 2^n+n } \right|$$

anonymous · Answer

hi dan is (a) part correct? and i'm stuck on (b) part