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Question Number 165372 Answers: 1 Comments: 0

lim_(x→+∞) ln (1+2^x )ln (1+(3/x))

$$\underset{{x}\rightarrow+\infty} {\mathrm{lim}ln}\:\left(\mathrm{1}+\mathrm{2}^{{x}} \right)\mathrm{ln}\:\left(\mathrm{1}+\frac{\mathrm{3}}{{x}}\right) \\ $$

Question Number 165370 Answers: 1 Comments: 1

Question Number 165364 Answers: 2 Comments: 0

Question Number 165362 Answers: 1 Comments: 0

Question Number 165361 Answers: 1 Comments: 2

Obtain a general formula for the sequence (2/3),(4/5),(8/9),((16)/(17)),((32)/(33)),... assuming the sequence continues in that pattern.

$$\mathrm{Obtain}\:\mathrm{a}\:\mathrm{general}\:\mathrm{formula}\:\mathrm{for} \\ $$$$\mathrm{the}\:\mathrm{sequence} \\ $$$$\:\frac{\mathrm{2}}{\mathrm{3}},\frac{\mathrm{4}}{\mathrm{5}},\frac{\mathrm{8}}{\mathrm{9}},\frac{\mathrm{16}}{\mathrm{17}},\frac{\mathrm{32}}{\mathrm{33}},... \\ $$$$\mathrm{assuming}\:\mathrm{the}\:\mathrm{sequence}\:\mathrm{continues}\:\mathrm{in}\:\mathrm{that} \\ $$$$\mathrm{pattern}. \\ $$

Question Number 165357 Answers: 1 Comments: 2

Question Number 165355 Answers: 1 Comments: 0

Question Number 165354 Answers: 0 Comments: 0

Question Number 165349 Answers: 1 Comments: 0

Question Number 165339 Answers: 1 Comments: 0

# Advanced Calculus # Let , f : R → Q is a continuous function . prove that ” f ” is a constant function . ■ m.n ∗ Adopted from mathematical analysis book ∗ −−−−−−−−−−−−−−

$$ \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:#\:{Advanced}\:\:\:{Calculus}\:#\:\:\: \\ $$$$\:\:\:\:\:\mathrm{L}{et}\:,\:\:{f}\::\:\mathbb{R}\:\rightarrow\:\mathbb{Q}\:\:{is}\:\:{a}\:\:{continuous} \\ $$$$\:\:\:\:\:\:{function}\:\:.\:{prove}\:{that}\:\:''\:{f}\:''\:{is}\:{a} \\ $$$$\:\:\:\:\:\:\:{constant}\:{function}\:.\:\:\:\:\:\:\:\:\:\blacksquare\:{m}.{n} \\ $$$$\:\:\:\:\:\:\:\ast\:{Adopted}\:{from}\:{mathematical}\:{analysis}\:{book}\:\:\ast\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:−−−−−−−−−−−−−− \\ $$$$ \\ $$

Question Number 165329 Answers: 2 Comments: 0

prove ( n∈ N ) 3(n+1) ∣ n^( 3) + (n+1)^( 3) + (n+2 )^( 3)

$$ \\ $$$$\:\:\:\:{prove}\:\:\:\:\:\:\:\:\:\:\left(\:{n}\in\:\mathbb{N}\:\right) \\ $$$$\:\:\:\:\mathrm{3}\left({n}+\mathrm{1}\right)\:\mid\:{n}^{\:\mathrm{3}} \:+\:\left({n}+\mathrm{1}\right)^{\:\mathrm{3}} +\:\left({n}+\mathrm{2}\:\right)^{\:\mathrm{3}} \\ $$$$ \\ $$

Question Number 165328 Answers: 3 Comments: 0

prove that Nice Integral 𝛗=∫_0 ^( 1) (( tan^( −1) (x^( (3/2)) ))/x^( 2) ) dx =((π + (√3) ln(7 +4(√3) ))/4) ■ m.n −−−−−−−−−

$$ \\ $$$$\:\:\:\:\:{prove}\:{that} \\ $$$$\:\: \\ $$$$\:\:\:\:\:\:\:\mathscr{N}{ice}\:\:\:\mathscr{I}{ntegral} \\ $$$$\:\:\:\:\:\:\:\boldsymbol{\phi}=\int_{\mathrm{0}} ^{\:\mathrm{1}} \frac{\:{tan}^{\:−\mathrm{1}} \:\left({x}^{\:\frac{\mathrm{3}}{\mathrm{2}}} \right)}{{x}^{\:\mathrm{2}} }\:{dx}\:\:=\frac{\pi\:+\:\sqrt{\mathrm{3}}\:{ln}\left(\mathrm{7}\:+\mathrm{4}\sqrt{\mathrm{3}}\:\right)}{\mathrm{4}}\:\:\:\:\:\:\:\:\:\:\:\:\:\blacksquare\:\:{m}.{n} \\ $$$$\:\:\:\:\:\:−−−−−−−−−\:\:\: \\ $$

Question Number 165322 Answers: 1 Comments: 2

who can prove that 2^n −1produces a prime number when n is a prime number

$${who}\:{can}\:{prove}\:{that}\:\mathrm{2}^{{n}} −\mathrm{1}{produces} \\ $$$${a}\:{prime}\:{number}\:{when}\:\:{n}\:\:{is}\:{a}\: \\ $$$${prime}\:{number} \\ $$

Question Number 165321 Answers: 2 Comments: 0

Question Number 165320 Answers: 1 Comments: 0

Ω = ∫_0 ^( (π/4)) cos (2x ).e^( ⌊ sin(x)+ cos(x) ⌋) dx ⌊ x ⌋= max { m ∈ Z ∣ m ≤ x } −−−−

$$ \\ $$$$\Omega\:=\:\int_{\mathrm{0}} ^{\:\frac{\pi}{\mathrm{4}}} \:{cos}\:\left(\mathrm{2}{x}\:\right).{e}^{\:\lfloor\:{sin}\left({x}\right)+\:{cos}\left({x}\right)\:\rfloor} {dx} \\ $$$$\:\:\:\lfloor\:{x}\:\rfloor=\:{max}\:\left\{\:{m}\:\in\:\mathbb{Z}\:\mid\:\:{m}\:\leqslant\:{x}\:\right\} \\ $$$$\:\:\:\:\:\:\:\:−−−− \\ $$

Question Number 165314 Answers: 0 Comments: 2

sin^2 1+sin^2 2+sin^2 3+.....+sin^2 90=?

$$\mathrm{sin}\:^{\mathrm{2}} \mathrm{1}+\mathrm{sin}\:^{\mathrm{2}} \mathrm{2}+\mathrm{sin}\:^{\mathrm{2}} \mathrm{3}+.....+{sin}^{\mathrm{2}} \mathrm{90}=? \\ $$

Question Number 165301 Answers: 1 Comments: 0

Question Number 165296 Answers: 2 Comments: 1

Question Number 165307 Answers: 0 Comments: 0

Question Number 165291 Answers: 1 Comments: 0

Question Number 165309 Answers: 0 Comments: 0

(6/(6+(√6))) + (6/(6^2 +(√6))) +(6/(6^3 +(√6))) +...+(6/(6^(1000) +(√6))) =?

$$\:\frac{\mathrm{6}}{\mathrm{6}+\sqrt{\mathrm{6}}}\:+\:\frac{\mathrm{6}}{\mathrm{6}^{\mathrm{2}} +\sqrt{\mathrm{6}}}\:+\frac{\mathrm{6}}{\mathrm{6}^{\mathrm{3}} +\sqrt{\mathrm{6}}}\:+...+\frac{\mathrm{6}}{\mathrm{6}^{\mathrm{1000}} +\sqrt{\mathrm{6}}}\:=? \\ $$

Question Number 165262 Answers: 2 Comments: 0

find the sum Σ_(n=1) ^∞ ((1/2))^n + i ( (1/3) )^n

$$\boldsymbol{{find}}\:\boldsymbol{{the}}\:\boldsymbol{{sum}}\:\underset{\boldsymbol{{n}}=\mathrm{1}} {\overset{\infty} {\sum}}\:\left(\frac{\mathrm{1}}{\mathrm{2}}\right)^{\boldsymbol{{n}}} \:+\:\boldsymbol{{i}}\:\left(\:\frac{\mathrm{1}}{\mathrm{3}}\:\right)^{\boldsymbol{{n}}} \: \\ $$

Question Number 165255 Answers: 1 Comments: 0

nice integral ∫_0 ^1 (1/x)ln(Σ_(m=0) ^n x^m )dx=? −−−−−−−−−−−−−by MATH.AMIN

Question Number 165243 Answers: 1 Comments: 0

⌊Find the value of x???⌋ ⌊5x + ((5x)/((5 + 5)^5 )) × (−5x) ÷ 555x −55x ×((5÷5)/5) + x = 555555555555555⌋ ^(proof:z.a)

$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\lfloor\boldsymbol{\mathrm{Find}}\:\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{value}}\:\boldsymbol{\mathrm{of}}\:\boldsymbol{{x}}???\rfloor \\ $$$$\:\:\:\lfloor\mathrm{5}\boldsymbol{{x}}\:+\:\frac{\mathrm{5}\boldsymbol{{x}}}{\left(\mathrm{5}\:+\:\mathrm{5}\right)^{\mathrm{5}} }\:×\:\left(−\mathrm{5}\boldsymbol{{x}}\right)\:\boldsymbol{\div}\:\mathrm{555}\boldsymbol{{x}}\:−\mathrm{55}\boldsymbol{{x}}\:×\frac{\mathrm{5}\boldsymbol{\div}\mathrm{5}}{\mathrm{5}}\:\:+\:\boldsymbol{{x}}\:=\:\mathrm{555555555555555}\rfloor \\ $$$$\:^{\mathrm{proof}:\mathrm{z}.\mathrm{a}} \\ $$

Question Number 165240 Answers: 1 Comments: 0

soit la serie de fonction Σ_(n=2 ) (x^n /(nx+ln(n))) etudie la convergence simple sur [0,1[

$$\:{soit}\:{la}\:{serie}\:{de}\:{fonction}\:\underset{{n}=\mathrm{2}\:\:\:} {\sum}\frac{{x}^{{n}} }{{nx}+{ln}\left({n}\right)} \\ $$$${etudie}\:{la}\:{convergence}\:{simple}\:{sur}\:\left[\mathrm{0},\mathrm{1}\left[\right.\right. \\ $$

Question Number 165234 Answers: 0 Comments: 1

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