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Question Number 122302 Answers: 3 Comments: 0

∫_0 ^∞ (dx/((1+x^2 )(4+x^2 )(16+x^2 )(64+x^2 )))

$$\int_{\mathrm{0}} ^{\infty} \frac{{dx}}{\left(\mathrm{1}+{x}^{\mathrm{2}} \right)\left(\mathrm{4}+{x}^{\mathrm{2}} \right)\left(\mathrm{16}+{x}^{\mathrm{2}} \right)\left(\mathrm{64}+{x}^{\mathrm{2}} \right)} \\ $$

Question Number 122317 Answers: 0 Comments: 0

1+9((1/4))^4 +17(((1.5)/(4.8)))^4 +25(((1.5.9)/(4.8.12)))^4 +...=(π/(2(√2)(Γ^2 ((3/4)))))

$$\mathrm{1}+\mathrm{9}\left(\frac{\mathrm{1}}{\mathrm{4}}\right)^{\mathrm{4}} +\mathrm{17}\left(\frac{\mathrm{1}.\mathrm{5}}{\mathrm{4}.\mathrm{8}}\right)^{\mathrm{4}} +\mathrm{25}\left(\frac{\mathrm{1}.\mathrm{5}.\mathrm{9}}{\mathrm{4}.\mathrm{8}.\mathrm{12}}\right)^{\mathrm{4}} +...=\frac{\pi}{\mathrm{2}\sqrt{\mathrm{2}}\left(\Gamma^{\mathrm{2}} \left(\frac{\mathrm{3}}{\mathrm{4}}\right)\right)} \\ $$

Question Number 122176 Answers: 2 Comments: 2

∫_0 ^(π/2) ((tanx))^(1/7) dx

$$\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \sqrt[{\mathrm{7}}]{{tanx}}\:{dx} \\ $$

Question Number 122377 Answers: 1 Comments: 4

Question Number 122069 Answers: 1 Comments: 0

∫_0 ^1 (1/( ((x^(96) −x^(97) ))^(1/(97)) ))dx

$$\int_{\mathrm{0}} ^{\mathrm{1}} \frac{\mathrm{1}}{\:\sqrt[{\mathrm{97}}]{{x}^{\mathrm{96}} −{x}^{\mathrm{97}} }}{dx} \\ $$

Question Number 122023 Answers: 1 Comments: 0

Σ_(n=0) ^∞ (((−1)^n F_n )/7^n ) (F_n denotes Fibbonocci sequence)

$$\underset{{n}=\mathrm{0}} {\overset{\infty} {\sum}}\frac{\left(−\mathrm{1}\right)^{{n}} {F}_{{n}} }{\mathrm{7}^{{n}} }\:\:\:\:\:\:\left({F}_{{n}} \:{denotes}\:{Fibbonocci}\:{sequence}\right) \\ $$

Question Number 122013 Answers: 0 Comments: 6

∫_0 ^(π/(24)) log(tanθ)dθ Problem source: brilliant

$$\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{24}}} {log}\left({tan}\theta\right){d}\theta \\ $$$${Problem}\:{source}:\:{brilliant} \\ $$

Question Number 121983 Answers: 1 Comments: 2

∫_0 ^(π/2) sin^n x dx (In closed form) (n∈N)

$$\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} {sin}^{{n}} {x}\:{dx}\:\left({In}\:{closed}\:{form}\right)\:\:\left({n}\in\mathbb{N}\right) \\ $$

Question Number 121914 Answers: 0 Comments: 1

∫_0 ^(π/2) (sinθ)^(−(1/n)) dθ

$$\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \left({sin}\theta\right)^{−\frac{\mathrm{1}}{{n}}} {d}\theta \\ $$

Question Number 121739 Answers: 1 Comments: 0

(1^(13) /(e^(2π) −1))+(2^(13) /(e^(4π) −1))+(3^(13) /(e^(6π) −1))+....

$$\frac{\mathrm{1}^{\mathrm{13}} }{{e}^{\mathrm{2}\pi} −\mathrm{1}}+\frac{\mathrm{2}^{\mathrm{13}} }{{e}^{\mathrm{4}\pi} −\mathrm{1}}+\frac{\mathrm{3}^{\mathrm{13}} }{{e}^{\mathrm{6}\pi} −\mathrm{1}}+.... \\ $$

Question Number 121697 Answers: 3 Comments: 0

Q. FACTORIZE− (1) 9x^2 +12xy+4y^2 (2) 25x^2 −20xy+16y^2 (3) 36x^2 +42xy+49y^2 ★★VISHAL★★

$$\:\mathbb{Q}.\:\mathbb{FACTORIZE}− \\ $$$$\:\left(\mathrm{1}\right)\:\mathrm{9x}^{\mathrm{2}} +\mathrm{12xy}+\mathrm{4y}^{\mathrm{2}} \\ $$$$\:\left(\mathrm{2}\right)\:\mathrm{25x}^{\mathrm{2}} −\mathrm{20xy}+\mathrm{16y}^{\mathrm{2}} \\ $$$$\:\left(\mathrm{3}\right)\:\mathrm{36x}^{\mathrm{2}} +\mathrm{42xy}+\mathrm{49y}^{\mathrm{2}} \\ $$$$\:\:\:\:\:\:\:\:\:\bigstar\bigstar\mathbb{VISHAL}\bigstar\bigstar \\ $$

Question Number 121678 Answers: 0 Comments: 0

Question Number 121677 Answers: 2 Comments: 1

Question Number 121659 Answers: 2 Comments: 4

∫_0 ^∞ (dx/((1+x^2 )(1+a^2 x^2 )(1+a^4 x^2 )(1+a^6 x^2 ).....))

$$\int_{\mathrm{0}} ^{\infty} \frac{{dx}}{\left(\mathrm{1}+{x}^{\mathrm{2}} \right)\left(\mathrm{1}+{a}^{\mathrm{2}} {x}^{\mathrm{2}} \right)\left(\mathrm{1}+{a}^{\mathrm{4}} {x}^{\mathrm{2}} \right)\left(\mathrm{1}+{a}^{\mathrm{6}} {x}^{\mathrm{2}} \right).....} \\ $$$$ \\ $$

Question Number 121655 Answers: 2 Comments: 2

Question Number 121653 Answers: 0 Comments: 5

((log1)/( (√1)))−((log3)/( (√3)))+((log5)/( (√5)))−((log7)/( (√7)))+....

$$\frac{{log}\mathrm{1}}{\:\sqrt{\mathrm{1}}}−\frac{{log}\mathrm{3}}{\:\sqrt{\mathrm{3}}}+\frac{{log}\mathrm{5}}{\:\sqrt{\mathrm{5}}}−\frac{{log}\mathrm{7}}{\:\sqrt{\mathrm{7}}}+.... \\ $$

Question Number 121454 Answers: 1 Comments: 2

1+(1/1^2 )+(1/2^2 )+...+(1/((1.2)^2 ))+(1/((2.3)^2 ))+...+(1/((1.2.3)^2 ))+(1/((2.3.4)^2 ))+...+(1/((1.2.3.4)^2 ))+..... Or 1+Σ_(n=1) ^∞ (1/n^2 )+Σ_(n=1) ^∞ (1/((n(n+1))^2 ))+Σ^∞ (1/((n(n+1)(n+2))^2 ))+.....

$$\mathrm{1}+\frac{\mathrm{1}}{\mathrm{1}^{\mathrm{2}} }+\frac{\mathrm{1}}{\mathrm{2}^{\mathrm{2}} }+...+\frac{\mathrm{1}}{\left(\mathrm{1}.\mathrm{2}\right)^{\mathrm{2}} }+\frac{\mathrm{1}}{\left(\mathrm{2}.\mathrm{3}\right)^{\mathrm{2}} }+...+\frac{\mathrm{1}}{\left(\mathrm{1}.\mathrm{2}.\mathrm{3}\right)^{\mathrm{2}} }+\frac{\mathrm{1}}{\left(\mathrm{2}.\mathrm{3}.\mathrm{4}\right)^{\mathrm{2}} }+...+\frac{\mathrm{1}}{\left(\mathrm{1}.\mathrm{2}.\mathrm{3}.\mathrm{4}\right)^{\mathrm{2}} }+..... \\ $$$$ \\ $$$${Or} \\ $$$$\mathrm{1}+\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{\mathrm{1}}{{n}^{\mathrm{2}} }+\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{\mathrm{1}}{\left({n}\left({n}+\mathrm{1}\right)\right)^{\mathrm{2}} }+\overset{\infty} {\sum}\frac{\mathrm{1}}{\left({n}\left({n}+\mathrm{1}\right)\left({n}+\mathrm{2}\right)\right)^{\mathrm{2}} }+..... \\ $$

Question Number 121326 Answers: 1 Comments: 3

((Σ_(n=1) ^∞ (1/(n^2 +1)))/(Σ_(n=2) ^∞ (1/(n^2 −1))))

$$\frac{\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{\mathrm{1}}{{n}^{\mathrm{2}} +\mathrm{1}}}{\underset{{n}=\mathrm{2}} {\overset{\infty} {\sum}}\frac{\mathrm{1}}{{n}^{\mathrm{2}} −\mathrm{1}}} \\ $$

Question Number 121229 Answers: 1 Comments: 0

Question Number 121217 Answers: 0 Comments: 0

Question Number 121215 Answers: 0 Comments: 0

Question Number 121085 Answers: 3 Comments: 1

Question Number 121044 Answers: 0 Comments: 0

(3/4)+(1/2)=..... { (),() :}

$$\frac{\mathrm{3}}{\mathrm{4}}+\frac{\mathrm{1}}{\mathrm{2}}=.....\begin{cases}{}\\{}\end{cases} \\ $$

Question Number 120727 Answers: 1 Comments: 0

Question Number 120631 Answers: 1 Comments: 0

Question Number 120598 Answers: 0 Comments: 0

Let A be a subset of a Real number with dimension 2 and let x be a real number member of dimension 2. Then x is called the limit point of A if ...?

$$ \\ $$$$\mathrm{Let}\:\mathrm{A}\:\mathrm{be}\:\mathrm{a}\:\mathrm{subset}\:\mathrm{of}\:\mathrm{a}\:\mathrm{Real}\:\mathrm{number} \\ $$$$\mathrm{wit}{h}\:\mathrm{dimension}\:\mathrm{2}\:\mathrm{and}\:\mathrm{let}\:\mathrm{x}\:\mathrm{be}\:\mathrm{a}\:\mathrm{real} \\ $$$$\mathrm{num}{b}\mathrm{er}\:\mathrm{member}\:\mathrm{of}\:\mathrm{dimension}\:\mathrm{2}.\:\mathrm{Then}\: \\ $$$$\mathrm{x}\:\mathrm{is}\:\mathrm{called}\:\mathrm{the}\:\mathrm{limit}\:\mathrm{point}\:\mathrm{of}\:\mathrm{A}\:\mathrm{if}\:...? \\ $$

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