How to show that $R^3$ is the direct sum of $W_1=$Span$(1,1,1)$ and $W_2=$Span$(\{1,0,0\}, \{1,1,0\})$?
114142
How to show that $\mathbb{R}^3$ is the direct sum of $W_1={\rm span}\{(1,1,1)\}$ and $W_2={\rm span}\{(1,0,0),(1,1,0)\}$?
106487
Let $S$ and $W$ be subsets of a vector space $V$. Show that if $S$ is a subset of $W$, then $\mathrm{span}(S)$ is a subspace of $\mathrm{span}(W)$
78473
Showing $ \sum_{n=0}^{\infty} \frac{1}{(3n+1)(3n+2)}=\frac{\pi}{3\sqrt{3}}$
11612
How to show that $\sum_{k=1}^n k(n+1-k)=\binom{n+2}3$?
63879
Prove that $\sum_{k=0}^r {m \choose k} {n \choose r-k} = {m+n \choose r}$
35625
Direct sum of orthogonal subspaces
135212
The square of an integer has form $3n$ or $3n+1$
14576
$(U\cap W)^0 = U^0 + W^0$
63474
Showing $\sum_{i = 1}^n\frac1{i(i+1)} = 1-\frac1{n+1}$ without induction?
122006
Proving combinatorial identity $\sum_{k=0}^{n}(-1)^k \binom{2n-k}k 2^{2n-2k} = 2n+1$ "directly"
124135
A general formula for $\sum (k-1)(k-2)(k-3)$?
121880
How to show that $|D_{2n}| = 2n$ via the presentation?
114173
Explanation of the formulas for sums $\sum nr^n$ and $\sum n^2 r^n$
21121
Express $w$ and $1/w$ for $w=\frac {\sqrt2+\sqrt3}{\sqrt5-\sqrt3}$ in the simplest form with a rational denominator
148442
Show that the sum $\sum_{k = 0}^n 2^k \binom{n}{k}$ is equal to $3^n$
20299
Is $k=3$ the only solution to $\sum_{r=1}^n r^k =\left( \sum_{r=1}^nr^1 \right)^2 $?
69498
What is $\sum_{r=0}^n \frac{(-1)^r}{\binom{n}{r}}$?