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Prove using the density of Q in R that every real number x is the limit of a cauchy sequence of rational numbers (r_n )_(n∈N) . Give a sequence of irrational numbers (S_n ) such that S_n → x.

$Prove using the density of Q in R that every real number x is the limit of$ $a cauchy sequence of rational numbers {(r_{n})}_{n \in N} . Give a sequence of irrational$ $numbers (S_{n}) such that S_{n} \to x .$

Question Number 11664 Answers: 2 Comments: 1

550÷11=50 And here 5^2 +5^2 +0^2 =50 find another three digit number which is divisible by 11 and the quotient is the sum of the square of the every digit of the dividend. /

$550 \div 11 = 50 A n d h e r e 5^{2} + 5^{2} + 0^{2} = 50$ $f i n d a n o t h e r t h r e e d i g i t n u m b e r$ $w h i c h i s d i v i s i b l e b y 11 a n d t h e$ $q u o t i e n t i s t h e s u m o f t h e$ $s q u a r e o f t h e e v e r y d i g i t o f$ $t h e d i v i d e n d .$ $/$

Question Number 11606 Answers: 1 Comments: 0

What is the smallest positive integer x for which (1/(32)) = (x/(10^y )) for some positive integer y ?

$What is the smallest positive integer x for$ $which \frac{1}{32} = \frac{x}{10^{y}} for some positive integer y ?$

Question Number 11365 Answers: 0 Comments: 1

∅(n)=n−1 , n∈Z ,where ∅ is Eular phi function. True or false .And explain it .

$\emptyset (n) = n - 1, n \in Z, where \emptyset is Eular phi function .$ $True or false . And explain it .$

Question Number 11321 Answers: 2 Comments: 2

How many solution {x, y, z} that fulfilled x + y + z = 99 ? x,y,z ∈ N

$How many solution {x, y, z} that fulfilled$ $x + y + z = 99 ?$ $x, y, z \in N$

Question Number 11139 Answers: 1 Comments: 1

Question Number 11075 Answers: 1 Comments: 6

Let n be the smallest positive integer that is a multiple of 75 and has exactly 75 positive integral divisors, including 1 and itself. Find (n/(75))

$Let n be the smallest positive integer that is$ $a multiple of 75 and has exactly 75 positive$ $integral divisors, including 1 and itself .$ $Find \frac{n}{75}$

Question Number 11048 Answers: 4 Comments: 0

Which one is largest? (without using calculator) 31^(11) or 17^(14) ??

$Which one is largest ? (without using calculator)$ $31^{11} or 17^{14} ? ?$

Question Number 10671 Answers: 2 Comments: 0

Σ_(n = 1) ^∞ 5((1/4))^(n − 1)

$\underset{n = 1}{\sum^{\infty}} 5 {(\frac{1}{4})}^{n - 1}$

Question Number 10670 Answers: 0 Comments: 0

Prove that: ζ(s)=Σ_(n=1) ^∞ n^(−s) =Π_(p∈P) ^∞ (1−p^(−s) )^(−1)

$Prove that :$ $ζ (s) = \underset{n = 1}{\sum^{\infty}} n^{- s} = \underset{p \in P}{\prod^{\infty}} {(1 - p^{- s})}^{- 1}$

Question Number 10665 Answers: 0 Comments: 2

nth prime = p_n nth non−prime = q_n Determine if q_n >p_n for ∀n≥2

$n th prime = p_{n}$ $n th non - prime = q_{n}$ $Determine if q_{n} > p_{n} for \forall n ⩾ 2$

Question Number 10664 Answers: 0 Comments: 0

S=Σ_(n∉P_(n≥1) ) ^∞ n Q=Σ_(n∈P_(n≥1) ) ^∞ n Prove if true: S>Q

$S = \underset{\underset{n ⩾ 1}{n \notin P}}{\sum^{\infty}} n$ $Q = \underset{\underset{n ⩾ 1}{n \in P}}{\sum^{\infty}} n$ $Prove if true :$ $S > Q$

Question Number 10662 Answers: 0 Comments: 0

determine if: (1/2^s )+(1/3^s )+(1/5^s )+...≥(1/1^s )+(1/4^s )+(1/6^s )+... or: Σ_(n∈P_(n≥1) ) ^∞ (1/n^s )≥Σ_(n∉P_(n≥1) ) ^∞ (1/n^s ), Re(s)>1 note: Σ_(n∈P_(n≥1) ) ^∞ (1/n^s )+Σ_(n∉P_(n≥1) ) ^∞ (1/n^s )=ζ(s)

$determine if :$ $\frac{1}{2^{s}} + \frac{1}{3^{s}} + \frac{1}{5^{s}} + . . . ⩾ \frac{1}{1^{s}} + \frac{1}{4^{s}} + \frac{1}{6^{s}} + . . .$ $or :$ $\underset{\underset{n ⩾ 1}{n \in P}}{\sum^{\infty}} \frac{1}{n^{s}} ⩾ \underset{\underset{n ⩾ 1}{n \notin P}}{\sum^{\infty}} \frac{1}{n^{s}}, Re (s) > 1$ $note :$ $\underset{\underset{n ⩾ 1}{n \in P}}{\sum^{\infty}} \frac{1}{n^{s}} + \underset{\underset{n ⩾ 1}{n \notin P}}{\sum^{\infty}} \frac{1}{n^{s}} = ζ (s)$