### Answers (110)

 22 Does $\sum\limits_{n=1}^\infty\frac{1}{\sqrt{n}+\sqrt{n+1}}$ converge? 18 The limit of $\tan(n)$ 17 Proving a trig identity: $\frac{\sin(A + B)}{\sin(A - B)}=\frac{\tan A + \tan B}{\tan A - \tan B}$ 16 If in a group $G$, we have $a^5 = e$ and $aba^{-1} = b^2$ for some $a$, $b$ in $G$, then what is the order of $b$? 15 A characteristic subgroup is a normal subgroup

### Reputation (6,862)

 +10 Relationship Between Basis For Vector Space And Basis For Dual Space -2 Prove that if $G$ is a tree, then $G^3$ is Hamiltonian. +10 The limit of $\tan(n)$ +10 Maximal order of an element in a symmetric group

### Questions (46)

 46 Example of a Borel set that is neither $F_\sigma$ nor $G_\delta$ 20 Why does $PSL(2,\mathbb C)\cong PGL(2,\mathbb C)$ but $PSL(2,\mathbb R) \not\cong PGL(2,\mathbb R)$? 13 Number of solutions of $x^2_1+\dots+x^2_n=0,$ $x_i\in \Bbb{F}_q.$ 11 Group with exactly two subgroups of index 2 6 Torsion subgroup of $SL(n,\mathbb Z)$

### Tags (89)

 162 abstract-algebra × 59 24 convergence-divergence × 2 157 group-theory × 59 23 linear-algebra × 18 58 calculus × 13 20 ring-theory × 7 32 finite-groups × 12 20 trigonometry × 3 29 sequences-and-series × 5 18 graph-theory × 11

### Bookmarks (10)

 46 Example of a Borel set that is neither $F_\sigma$ nor $G_\delta$ 34 Is it true in an arbitrary field that $-1$ is a sum of two squares iff it is a sum of three squares? 9 The limit of $\tan(n)$ 4 Condition for a vertex-transitive graph to be symmetric 4 Maximal ideal of ring of matrices

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