MathDB

Problem 2

Part of 2006 VJIMC

Problems(2)

if sum(a_n/n) converges then sum(a_n)/n converges

Source: VJIMC 2006 1.2

6/28/2021
Suppose that (an)(a_n) is a sequence of real numbers such that the series ∑n=1∞ann\sum_{n=1}^\infty\frac{a_n}nis convergent. Show that the sequence bn=1n∑j=1najb_n=\frac1n\sum^n_{j=1}a_jis convergent and find its limit.
limitsConvergence
group is only squares iff |G| is odd

Source: VJIMC 2006 2.2

6/28/2021
Let (G,⋅)(G,\cdot) be a finite group of order nn. Show that each element of GG is a square if and only if nn is odd.
group theoryabstract algebra