# Math Help - SUm

1. ## SUm

Find the first three terms and the nth term of the series with the sum to n terms , $S_n$ , given by :

(1) $S_n=4n-\frac{1}{n}$

I know the first three terms . The answer given by the book for the nth term is :

$4+\frac{1}{n(n-1)},n>1$

My question is if that's the answer , why can't i get the first term which is 3 when i substitute n=1 into the formula .

And if it says n is greater than 1 , then there is no way to find the first term.

2. Originally Posted by thereddevils
Find the first three terms and the nth term of the series with the sum to n terms , $S_n$ , given by :

(1) $S_n=4n-\frac{1}{n}$

I know the first three terms . The answer given by the book for the nth term is :

$4+\frac{1}{n(n-1)},n>1$

My question is if that's the answer , why can't i get the first term which is 3 when i substitute n=1 into the formula .

And if it says n is greater than 1 , then there is no way to find the first term.
The form for the general term $a_n$ only applies to $n>1$ (you need $S_{n-1}$ to get this from the sum to $n$ terms so only applies when $S_{n-1}$ is given by the formula. But $S_0=0$ so the first term:

$a_1=S_1$

CB