Finding the General Term for a Sequence with a Given Sum?

[LAdidadida]

Homework Statement

Find the general term of a sequence whose sum of the first n terms is S(n)=1/n(n+1)

Homework Equations

N/A

The Attempt at a Solution

I am able to work out T(n) as through T(n)=S(n)-S(n-1)
which works out to be -2/n(n-1)(n+1) however this doesn't work for when n=1

Any help would be greatly appreciated

 

[f(x)]

Homework Statement

Find the general term of a sequence whose sum of the first n terms is S(n)=1/n(n+1)

Homework Equations

N/A

The Attempt at a Solution

I am able to work out T(n) as through T(n)=S(n)-S(n-1)
which works out to be -2/n(n-1)(n+1) however this doesn't work for when n=1

Any help would be greatly appreciated

expression you derived is from T(n)=S(n)-S(n-1) => T(1)=S(1)-S(0)
T(1)=S(1) , S(0) doesn't make sense.

T(1) can be directly calculated from general expression for S(n) for n=1

 

[HallsofIvy]

In other words, since a sum cannot have 0 terms, there is no such thing as S(0)! The first partial sum is S(1)= T(1).