For $\sum^n_{i=1} \frac1{i(i+1)}$ Find a formula and proofs that it holds for all n ≥ 1.
How would I find the formula for this one that can hold for all n ≥ 1?
Use Mathematical induction to prove that for all integers, $n$ is greater than or equal to $1$. I am confused on what to do after I do the the basis step that is using $n$ as $1$.
$$\frac{1}{1 \cdot 2} + \frac{1}{2 \cdot 3} +...+\frac{1}{n(n+1)}=1-\frac{1}{n+1}$$
Since $n!$ represents $$1\cdot2\cdot3\cdots n,$$ I am wondering if there is a way to represent $$1+2+3+\dots+n?$$
What are some usual notations for the computation of some common sequences? Any other examples?
(Pardon if this seems a bit beginner, this is my first post in math - trying to improve my knowledge while tackling Project Euler problems)
I'm aware of Sigma notation, but is there a function/name for e.g.
$$ 4 + 3 + 2 + 1 \longrightarrow 10 ,$$
similar to $$4! = 4 \cdot 3 \cdot 2 \cdot 1 ,$$...
Use Mathematical induction to prove that for all integers, $n$ is greater than or equal to $1$. I am confused on what to do after I do the the basis step that is using $n$ as $1$.
$$\frac{1}{1 \cdot 2} + \frac{1}{2 \cdot 3} +...+\frac{1}{n(n+1)}=1-\frac{1}{n+1}$$
(Pardon if this seems a bit beginner, this is my first post in math - trying to improve my knowledge while tackling Project Euler problems)
I'm aware of Sigma notation, but is there a function/name for e.g.
$$ 4 + 3 + 2 + 1 \longrightarrow 10 ,$$
similar to $$4! = 4 \cdot 3 \cdot 2 \cdot 1 ,$$...
