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Question Number 207930 Answers: 0 Comments: 1

a_n number series a_(k+3) ^2 + a_k = a_(k+2) + a_(k+7) find: k = ?

$$\mathrm{a}_{\boldsymbol{\mathrm{n}}} \:\:\:\mathrm{number}\:\mathrm{series} \\ $$$$\mathrm{a}_{\boldsymbol{\mathrm{k}}+\mathrm{3}} ^{\mathrm{2}} \:\:+\:\:\mathrm{a}_{\boldsymbol{\mathrm{k}}} \:\:=\:\:\mathrm{a}_{\boldsymbol{\mathrm{k}}+\mathrm{2}} \:\:+\:\:\mathrm{a}_{\boldsymbol{\mathrm{k}}+\mathrm{7}} \\ $$$$\mathrm{find}:\:\:\:\boldsymbol{\mathrm{k}}\:=\:? \\ $$

Question Number 207925 Answers: 1 Comments: 0

Question Number 207924 Answers: 0 Comments: 0

∫f(x)g(x)dx=Σ_(n=0) ^∞ (−1)^n lim_(h→0) (1/h^n ) Σ_(i=o) ^n [ (−1)^i (((n!)/(i!(n−i)!)))f(x+(n−i)h)] (1/(n!))∫_a ^x (x−t)^n g(t)dt prove that right its a relation that i have derrived

$$\int{f}\left({x}\right){g}\left({x}\right){dx}=\underset{{n}=\mathrm{0}} {\overset{\infty} {\sum}}\:\left(−\mathrm{1}\right)^{{n}} \:\underset{{h}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{1}}{{h}^{{n}} }\:\underset{{i}={o}} {\overset{{n}} {\sum}}\left[\:\left(−\mathrm{1}\right)^{{i}} \left(\frac{{n}!}{{i}!\left({n}−{i}\right)!}\right){f}\left({x}+\left({n}−{i}\right){h}\right)\right]\:\frac{\mathrm{1}}{{n}!}\underset{{a}} {\overset{{x}} {\int}}\left({x}−{t}\right)^{{n}} {g}\left({t}\right){dt}\: \\ $$$${prove}\:{that}\:{right} \\ $$$${its}\:{a}\:{relation}\:{that}\:{i}\:{have}\:{derrived} \\ $$

Question Number 207910 Answers: 1 Comments: 0

Question Number 207909 Answers: 0 Comments: 0

Question Number 207919 Answers: 1 Comments: 1

⇃

$$\:\:\:\:\downharpoonleft\underline{\:} \\ $$

Question Number 207906 Answers: 1 Comments: 0

help ∫_1 ^( ∞) x^(−ln(x)) dx

$${help} \\ $$$$\int_{\mathrm{1}} ^{\:\infty} {x}^{−{ln}\left({x}\right)} {dx} \\ $$$$ \\ $$

Question Number 207904 Answers: 0 Comments: 2

Question Number 207901 Answers: 1 Comments: 0

Question Number 207897 Answers: 3 Comments: 0

Find: (√(12 ∙ 13 ∙ 14 ∙ 15 + 1)) = ?

$$\mathrm{Find}: \\ $$$$\sqrt{\mathrm{12}\:\:\centerdot\:\:\mathrm{13}\:\:\centerdot\:\:\mathrm{14}\:\:\centerdot\:\:\mathrm{15}\:\:+\:\:\mathrm{1}}\:\:=\:\:? \\ $$

Question Number 207885 Answers: 0 Comments: 7

Find: i^4 + i^8 + i^(12) + i^(16) + i^(20) + i^(24) +...+ i^(100) = ?

$$\mathrm{Find}: \\ $$$$\boldsymbol{\mathrm{i}}^{\mathrm{4}} \:+\:\boldsymbol{\mathrm{i}}^{\mathrm{8}} \:+\:\boldsymbol{\mathrm{i}}^{\mathrm{12}} \:+\:\boldsymbol{\mathrm{i}}^{\mathrm{16}} \:+\:\boldsymbol{\mathrm{i}}^{\mathrm{20}} \:+\:\boldsymbol{\mathrm{i}}^{\mathrm{24}} \:+...+\:\boldsymbol{\mathrm{i}}^{\mathrm{100}} \:=\:? \\ $$

Question Number 207876 Answers: 1 Comments: 1

Find: ln (((2 tg 22,30°)/(1 − tg^2 22,30°))) = ?

$$\mathrm{Find}:\:\:\:\mathrm{ln}\:\left(\frac{\mathrm{2}\:\mathrm{tg}\:\mathrm{22},\mathrm{30}°}{\mathrm{1}\:−\:\mathrm{tg}^{\mathrm{2}} \:\mathrm{22},\mathrm{30}°}\right)\:=\:? \\ $$

Question Number 207879 Answers: 1 Comments: 0

Question Number 207878 Answers: 2 Comments: 0

Question Number 207866 Answers: 2 Comments: 0

If the system { ((y=−mx^2 −2)),((4x^2 +y^2 = 4)) :} have only one solution them m = (A) (1/3) (B)(1/( (√2))) (C) 1 (D) (√2) (E) (√3)

$$\:\:\:\mathrm{If}\:\mathrm{the}\:\mathrm{system}\:\begin{cases}{\mathrm{y}=−\mathrm{mx}^{\mathrm{2}} −\mathrm{2}}\\{\mathrm{4x}^{\mathrm{2}} +\mathrm{y}^{\mathrm{2}} =\:\mathrm{4}}\end{cases} \\ $$$$\:\:\mathrm{have}\:\mathrm{only}\:\mathrm{one}\:\mathrm{solution}\: \\ $$$$\:\:\mathrm{them}\:\mathrm{m}\:=\: \\ $$$$\:\:\left(\mathrm{A}\right)\:\frac{\mathrm{1}}{\mathrm{3}}\:\:\:\left(\mathrm{B}\right)\frac{\mathrm{1}}{\:\sqrt{\mathrm{2}}}\:\:\:\left(\mathrm{C}\right)\:\mathrm{1}\:\:\:\:\left(\mathrm{D}\right)\:\sqrt{\mathrm{2}}\:\:\:\left(\mathrm{E}\right)\:\sqrt{\mathrm{3}} \\ $$$$\:\: \\ $$

Question Number 207864 Answers: 1 Comments: 0

$$\:\:\:\:\:\underbrace{\:} \\ $$

Question Number 207858 Answers: 0 Comments: 1

calculer (1−a)^k /k∈N^

$${calculer}\:\left(\mathrm{1}−{a}\right)^{{k}} \:\:/{k}\in\overset{} {{N}} \\ $$

Question Number 207857 Answers: 1 Comments: 0

∫xtan^(−1) xdx

$$\int{x}\mathrm{tan}^{−\mathrm{1}} {xdx} \\ $$

Question Number 207852 Answers: 2 Comments: 0

Question Number 207846 Answers: 1 Comments: 0

Question Number 207845 Answers: 2 Comments: 0

Find: 1 + (1/(1+2)) + (1/(1+2+3)) +...+ (1/(1+2+3+...+40))

$$\mathrm{Find}: \\ $$$$\mathrm{1}\:+\:\frac{\mathrm{1}}{\mathrm{1}+\mathrm{2}}\:+\:\frac{\mathrm{1}}{\mathrm{1}+\mathrm{2}+\mathrm{3}}\:+...+\:\frac{\mathrm{1}}{\mathrm{1}+\mathrm{2}+\mathrm{3}+...+\mathrm{40}} \\ $$

Question Number 207842 Answers: 1 Comments: 0

(−1)^∞ =?

$$\left(−\mathrm{1}\right)^{\infty} =? \\ $$

Question Number 207834 Answers: 1 Comments: 0

$$\:\:\:\:\underbrace{\:} \\ $$$$ \\ $$

Question Number 207833 Answers: 0 Comments: 0

Question Number 207832 Answers: 1 Comments: 1

Prove that Sgn(0)=0

$${Prove}\:{that}\:{Sgn}\left(\mathrm{0}\right)=\mathrm{0} \\ $$

Question Number 207825 Answers: 3 Comments: 0

calculer (1−a)^(k ) :k∈N

$${calculer}\:\left(\mathrm{1}−{a}\right)^{{k}\:\:} \::{k}\in{N} \\ $$

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