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AllQuestion and Answers: Page 71

Question Number 209385 Answers: 1 Comments: 0

Question Number 209380 Answers: 0 Comments: 0

Question Number 209359 Answers: 3 Comments: 2

Question Number 209358 Answers: 1 Comments: 3

Question Number 209357 Answers: 3 Comments: 0

Evaluate : B_n = Π_(k=3) ^n (( k^( 2) −1)/(k^2 + k −6))= ?

$$ \\ $$$$\:\:\:\:\:\:{Evaluate}\:: \\ $$$$ \\ $$$$\:\:\:\:\:\mathrm{B}_{{n}} =\:\underset{{k}=\mathrm{3}} {\overset{{n}} {\prod}}\:\frac{\:{k}^{\:\mathrm{2}} −\mathrm{1}}{{k}^{\mathrm{2}} \:+\:{k}\:−\mathrm{6}}=\:? \\ $$

Question Number 209356 Answers: 1 Comments: 0

Evaluate : lim_( n→∞) Π_(k=0) ^(n−1) cos (((2^( k) .π)/(2^( n) −1)) ) = ?

$$ \\ $$$$\:\:\:\:\:{Evaluate}\:: \\ $$$$ \\ $$$$ \\ $$$$\:\:\:\:\mathrm{lim}_{\:{n}\rightarrow\infty} \:\underset{{k}=\mathrm{0}} {\overset{{n}−\mathrm{1}} {\prod}}\:{cos}\:\left(\frac{\mathrm{2}^{\:{k}} .\pi}{\mathrm{2}^{\:{n}} \:−\mathrm{1}}\:\right)\:\:=\:?\:\:\:\:\:\:\:\:\:\: \\ $$$$ \\ $$

Question Number 209353 Answers: 1 Comments: 0

Question Number 209352 Answers: 2 Comments: 0

Question Number 209347 Answers: 1 Comments: 0

Question Number 209342 Answers: 1 Comments: 0

Question Number 209341 Answers: 2 Comments: 0

solve x^(log 27) + 9^(log x) = 36

$$\mathrm{solve}\:\:\:\:\mathrm{x}^{\mathrm{log}\:\mathrm{27}} \:\:+\:\:\mathrm{9}^{\mathrm{log}\:\mathrm{x}} \:\:=\:\:\:\mathrm{36} \\ $$

Question Number 209336 Answers: 1 Comments: 1

Question Number 209332 Answers: 3 Comments: 0

Question Number 209320 Answers: 0 Comments: 0

Question Number 209318 Answers: 2 Comments: 0

Question Number 209316 Answers: 1 Comments: 0

if 2n^2 +3n^3 =n! find n

$$\boldsymbol{\mathrm{if}}\:\:\mathrm{2}\boldsymbol{\mathrm{n}}^{\mathrm{2}} +\mathrm{3}\boldsymbol{\mathrm{n}}^{\mathrm{3}} =\boldsymbol{\mathrm{n}}! \\ $$$$\boldsymbol{\mathrm{find}}\:\boldsymbol{\mathrm{n}} \\ $$

Question Number 209314 Answers: 0 Comments: 11

Question Number 209309 Answers: 0 Comments: 0

m , n ∈ N m ≥ 2 and n ≥ 2 p > 0 and q > 0 p + q = 1 Prove that: (1−q^n )^m + (1−p^m )^n ≥ 1

$$\mathrm{m}\:,\:\mathrm{n}\:\in\:\mathbb{N} \\ $$$$\mathrm{m}\:\geqslant\:\mathrm{2}\:\:\:\mathrm{and}\:\:\:\mathrm{n}\:\geqslant\:\mathrm{2} \\ $$$$\mathrm{p}\:>\:\mathrm{0}\:\:\:\mathrm{and}\:\:\:\mathrm{q}\:>\:\mathrm{0} \\ $$$$\mathrm{p}\:+\:\mathrm{q}\:=\:\mathrm{1} \\ $$$$\mathrm{Prove}\:\mathrm{that}:\:\:\:\left(\mathrm{1}−\mathrm{q}^{\boldsymbol{\mathrm{n}}} \right)^{\boldsymbol{\mathrm{m}}} \:+\:\left(\mathrm{1}−\mathrm{p}^{\boldsymbol{\mathrm{m}}} \right)^{\boldsymbol{\mathrm{n}}} \:\geqslant\:\mathrm{1} \\ $$

Question Number 209308 Answers: 1 Comments: 0

Donner l′e^ quivalence simple de I_n =∫^( 1) _( 0) (t^n /(t^n −t+1))dt

$$\mathrm{Donner}\:\mathrm{l}'\acute {\mathrm{e}quivalence}\:\mathrm{simple} \\ $$$$\mathrm{de}\:\mathrm{I}_{\mathrm{n}} =\underset{\:\mathrm{0}} {\int}^{\:\mathrm{1}} \frac{{t}^{{n}} }{{t}^{{n}} −{t}+\mathrm{1}}{dt} \\ $$

Question Number 209307 Answers: 2 Comments: 3

Question Number 209304 Answers: 1 Comments: 0

Question Number 209301 Answers: 0 Comments: 0

Question Number 209290 Answers: 0 Comments: 1

a^2 −a−^(1000) (√((1+8000a)))=1000 find a

$$\boldsymbol{\mathrm{a}}^{\mathrm{2}} −\boldsymbol{\mathrm{a}}−^{\mathrm{1000}} \sqrt{\left(\mathrm{1}+\mathrm{8000}\boldsymbol{\mathrm{a}}\right)}=\mathrm{1000} \\ $$$$\boldsymbol{\mathrm{find}}\:\boldsymbol{\mathrm{a}} \\ $$

Question Number 209289 Answers: 1 Comments: 0

Question Number 209288 Answers: 1 Comments: 0

Question Number 209281 Answers: 2 Comments: 2

Find the value of r, if ^(10) C_r = ^(10) C_(2r + 1)

$$\mathrm{Find}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\mathrm{r},\:\mathrm{if}\:\:\overset{\mathrm{10}} {\:}\mathrm{C}_{\mathrm{r}} \:\:=\:\:\overset{\mathrm{10}} {\:}\mathrm{C}_{\mathrm{2r}\:\:+\:\:\mathrm{1}} \\ $$

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