Find $A_n$ in finite form Find $A_n$ in nite form for $A_{n+1} - A_n = \frac{1}{n(n+1)}$ Or in other words, in the form such that the number of terms does not grow with n in each of the following cases

**Hint**

$$A_{n+1} - A_n = \frac{1}{n(n+1)}=\frac{1}{n}-\frac{1}{n+1}$$ makes $$A_{n+1}+\frac{1}{n+1}=A_n+\frac{1}{n}$$ Defining $B_n=A_n+\frac 1n$, this then leads to $$B_{n+1}=B_n=c$$ So $$ A_n+\frac{1}{n}=c \implies A_n=c-\frac{1}{n}$$