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Question Number 216914 Answers: 2 Comments: 0

Prove that: (1/(1001)) + (1/(1002)) + ... + (1/(2000)) > (5/8)

$Prove that :$ $\frac{1}{1001} + \frac{1}{1002} + . . . + \frac{1}{2000} > \frac{5}{8}$

Question Number 216913 Answers: 1 Comments: 0

6(1/4)%

$6 \frac{1}{4} %$

Question Number 216912 Answers: 0 Comments: 0

Find all three-digit numbers n such that 1. n is divisible by the sum of its digits. 2. n is a perfect square.

$Find all three - digit numbers n such that$ $1 . n is divisible by the sum of its digits .$ $2 . n is a perfect square .$

Question Number 216911 Answers: 1 Comments: 0

Find all positive integer x,y such that x^2 + y^2 + xy = 169

$F i n d a l l p o s i t i v e i n t e g e r x, y s u c h t h a t$ $x^{2} + y^{2} + xy = 169$

Question Number 216910 Answers: 0 Comments: 0

Ed:.06 a function δ(x) is a composite function which is as follow [{(f ○ g)(x)} ○ {(g ○ f)(x)}] ○ [{(f ′ ○ g ′)(x)} ○ {(g ′ ○ f ′)(x)}] where f(x) = Π_(n = 1) ^∞ ((nx^3 − nx^2 − nx −n)/(n^3 x − n^2 x − nx −x)) g(x)= f ′′(x) ∫_( ψ) ^( δ) δ(x) dx ∈ R\Q ? true or false?

$E d : . 06$ $a f u n c t i o n δ (x) i s a c o m p o s i t e f u n c t i o n$ $w h i c h i s a s f o l l o w$ $[{(f \circ g) (x)} \circ {(g \circ f) (x)}] \circ [{(f^{'} \circ g^{'}) (x)} \circ {(g^{'} \circ f^{'}) (x)}]$ $w h e r e$ $f (x) = \underset{n = 1}{\prod^{\infty}} \frac{{n x}^{3} - {n x}^{2} - n x - n}{n^{3} x - n^{2} x - n x - x}$ $g (x) = f^{″} (x)$ $\int_{ψ} \overset{δ}{} δ (x) d x \in R ∖ Q ?$ $t r u e o r f a l s e ?$

Question Number 216907 Answers: 1 Comments: 0

Prove:n!=1+Σ_(k=1) ^∞ (k^n /e^k )−Σ_(k=1) ^∞ ((B_k sin(πk)(n−k)!)/(πk))

$Prove : n! = 1 + \underset{k = 1}{\sum^{\infty}} \frac{k^{n}}{e^{k}} - \underset{k = 1}{\sum^{\infty}} \frac{B_{k} \sin (π k) (n - k)!}{π k}$

Question Number 216906 Answers: 0 Comments: 0

Prove:Γ(x)=(x^x /((2π)^(x−1) ))Π_(k=1) ^∞ (k^(2(x−1)) /(Π_(i=1) ^(x−1) [k^2 −((i/2))^2 ]))

$Prove : Γ (x) = \frac{x^{x}}{{(2 π)}^{x - 1}} \underset{k = 1}{\prod^{\infty}} \frac{k^{2 (x - 1)}}{\underset{i = 1}{\prod^{x - 1}} [k^{2} - {(\frac{i}{2})}^{2}]}$

Question Number 216900 Answers: 0 Comments: 1

Question Number 216886 Answers: 0 Comments: 1

Evaluate ((Σ_(k=1) ^(10) (∫_0 ^k (4u+1)du))/(5^2 Σ_(n=1) ^∞ (1/2)(Σ_(n=2) ^∞ (2/(m^2 +2m)))^(n−1) ))∫_(sin^(−1) (((−(√2))/2))) ^((π/2)cos(π/2)) (((1−secθsinθ)/((tanθ+cotθ)/(ϱ^θ −ϱ^(πi) ))))dθ

$E v a l u a t e \frac{\underset{k = 1}{\sum^{10}} (\int_{0}^{k} (4 u + 1) d u)}{5^{2} \underset{n = 1}{\sum^{\infty}} \frac{1}{2} {(\underset{n = 2}{\sum^{\infty}} \frac{2}{m^{2} + 2 m})}^{n - 1}} \int_{{s i n}^{- 1} (\frac{- \sqrt{2}}{2})}^{\frac{π}{2} c o s \frac{π}{2}} (\frac{1 - s e c θ s i n θ}{\frac{t a n θ + c o t θ}{ϱ^{θ} - ϱ^{π i}}}) d θ$

Question Number 216887 Answers: 0 Comments: 0

Π_(k=1) ^n cos((x/2^k ))=Pn(x) evaluate Pn(x) and P_n (x^2 +1)

$\underset{k = 1}{\prod^{n}} c o s (\frac{x}{2^{k}}) = P n (x)$ $e v a l u a t e P n (x) a n d P_{n} (x^{2} + 1)$

Question Number 216875 Answers: 1 Comments: 0

Let p be a prime number greater than 3. Prove that p^2 − 1 is always divisible by 24.

$Let p be a prime number greater than 3 . Prove that p^{2} - 1$ $is always divisible by 24 .$

Question Number 216861 Answers: 0 Comments: 0

Question Number 216859 Answers: 1 Comments: 3

Question Number 216855 Answers: 2 Comments: 0

Question Number 216842 Answers: 1 Comments: 0

Find all pairs of positive integers x, y that satisfy the system xy + x + y=71 x^2 y + xy^2 =880

$Find all pairs of positive integers x, y that satisfy$ $the system$ $xy + x + y = 71$ $x^{2} y + {xy}^{2} = 880$

Question Number 216841 Answers: 1 Comments: 0

Prove that: δ(n) = Σ_(d/n) 𝛟(d) 𝛕((n/d)) 𝛅(n) = Σ_(d/n) d , 𝛕(n) = Σ_(d/n) l and ϕ-Eyler.f

$Prove that : δ (n) = \sum_{\frac{d}{n}} φ (d) τ (\frac{n}{d})$ $δ (n) = \sum_{\frac{d}{n}} d, τ (n) = \sum_{\frac{d}{n}} l and φ - Eyler . f$

Question Number 216836 Answers: 3 Comments: 0

Find: (((1 + tan1°)(1 + tan2°)...(1 + tan44°))/((1−tan46°)(1−tan47°)...(1−tan89°))) = ?

$Find :$ $\frac{(1 + \tan 1 °) (1 + \tan 2 °) . . . (1 + \tan 44 °)}{(1 - \tan 46 °) (1 - \tan 47 °) . . . (1 - \tan 89 °)} = ?$

Question Number 216830 Answers: 1 Comments: 1

Prove:∀x∈R,∣cos x∣+∣cos 2x∣+…+∣cos nx∣≥((n−1)/2)(n∈Z_(>0) )

$Prove : \forall x \in R, ∣ \cos x ∣ + ∣ \cos 2 x ∣ + \dots + ∣ \cos n x ∣\geq \frac{n - 1}{2} (n \in Z_{> 0})$

Question Number 216827 Answers: 1 Comments: 1

Question Number 216821 Answers: 0 Comments: 0

Question Number 216820 Answers: 2 Comments: 0

f(x) = ax^4 + bx^3 + cx^2 + dx + e f(1) = 2 f(2) = 3 f(3) = 4 f(4) = 5 f(0) = 25 Then f(5) = ? Help me, please

$f (x) = {a x}^{4} + {b x}^{3} + {c x}^{2} + d x + e$ $f (1) = 2$ $f (2) = 3$ $f (3) = 4$ $f (4) = 5$ $f (0) = 25$ $T h e n f (5) = ?$ $H e l p m e, p l e a s e$

Question Number 216819 Answers: 0 Comments: 0

Prove:∫_(0 ) ^1 ((K(x))/( (√(3−x))))dx=(1/(96π(√3)))×Γ((1/(24)))Γ((3/(24)))Γ((7/(24)))Γ(((11)/(24)))

$Prove : \int_{0}^{1} \frac{K (x)}{\sqrt{3 - x}} d x = \frac{1}{96 π \sqrt{3}} \times Γ (\frac{1}{24}) Γ (\frac{3}{24}) Γ (\frac{7}{24}) Γ (\frac{11}{24})$

Question Number 216810 Answers: 0 Comments: 1

40 random numbers picked from 0 to 100. what is the probability that at least half of them has the range of 10.

Question Number 216800 Answers: 1 Comments: 0

Question Number 216799 Answers: 1 Comments: 1

Question Number 216807 Answers: 1 Comments: 0

Uh guys is the speed formula (d/t) or lim_(Δt→0) ((Δd)/(Δt))

$Uh guys is the speed formula$ $\frac{d}{t}$ $or$ $li \underset{Δ t \to 0}{m} \frac{Δ d}{Δ t}$

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