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Question Number 97985    Answers: 2   Comments: 0

let S_n =Σ_(k=1) ^n (1/(√(n^2 +2kn))) find lim_(n→+∞) S_n

$$\mathrm{let}\:\mathrm{S}_{\mathrm{n}} =\sum_{\mathrm{k}=\mathrm{1}} ^{\mathrm{n}} \:\frac{\mathrm{1}}{\sqrt{\mathrm{n}^{\mathrm{2}} +\mathrm{2kn}}} \\ $$$$\mathrm{find}\:\mathrm{lim}_{\mathrm{n}\rightarrow+\infty} \:\mathrm{S}_{\mathrm{n}} \\ $$

Question Number 97984    Answers: 2   Comments: 0

calculate Σ_(k=0) ^n (((−1)^k )/(2k+1)) C_n ^k

$$\mathrm{calculate}\:\sum_{\mathrm{k}=\mathrm{0}} ^{\mathrm{n}} \:\frac{\left(−\mathrm{1}\right)^{\mathrm{k}} }{\mathrm{2k}+\mathrm{1}}\:\mathrm{C}_{\mathrm{n}} ^{\mathrm{k}} \\ $$

Question Number 97983    Answers: 0   Comments: 0

f continue on [0,1] and f(x)>0 on [0,1] prove that ∫_0 ^1 lnf(x)dx≤ln(∫_0 ^1 f(x)dx)

$$\mathrm{f}\:\mathrm{continue}\:\:\mathrm{on}\:\left[\mathrm{0},\mathrm{1}\right]\:\mathrm{and}\:\mathrm{f}\left(\mathrm{x}\right)>\mathrm{0}\:\mathrm{on}\:\left[\mathrm{0},\mathrm{1}\right] \\ $$$$\mathrm{prove}\:\mathrm{that}\:\int_{\mathrm{0}} ^{\mathrm{1}} \mathrm{lnf}\left(\mathrm{x}\right)\mathrm{dx}\leqslant\mathrm{ln}\left(\int_{\mathrm{0}} ^{\mathrm{1}} \mathrm{f}\left(\mathrm{x}\right)\mathrm{dx}\right) \\ $$

Question Number 97981    Answers: 1   Comments: 0

calculate lim_(x→1^+ ) ∫_(x−1) ^(x^2 −1) (dt/(ln(1+t)))

$$\mathrm{calculate}\:\mathrm{lim}_{\mathrm{x}\rightarrow\mathrm{1}^{+} } \:\:\int_{\mathrm{x}−\mathrm{1}} ^{\mathrm{x}^{\mathrm{2}} −\mathrm{1}} \:\frac{\mathrm{dt}}{\mathrm{ln}\left(\mathrm{1}+\mathrm{t}\right)} \\ $$

Question Number 97979    Answers: 0   Comments: 0

find lim_(n→+∞) (C_(2n) ^n )^(1/n)

$$\mathrm{find}\:\mathrm{lim}_{\mathrm{n}\rightarrow+\infty} \:\left(\mathrm{C}_{\mathrm{2n}} ^{\mathrm{n}} \right)^{\frac{\mathrm{1}}{\mathrm{n}}} \\ $$

Question Number 97972    Answers: 3   Comments: 0

Prove that, (d/dx)(e^x ) = e^x

$$\:\:\:\:\mathrm{Prove}\:\mathrm{that}, \\ $$$$\:\:\:\:\:\frac{\boldsymbol{{d}}}{\boldsymbol{{dx}}}\left(\boldsymbol{{e}}^{\boldsymbol{{x}}} \right)\:=\:\boldsymbol{{e}}^{\boldsymbol{{x}}} \\ $$

Question Number 97968    Answers: 1   Comments: 1

$$ \\ $$

Question Number 99300    Answers: 1   Comments: 0

Find Σ_(n=1) ^∞ (1/((3n)!))=?

$$\mathrm{Find}\:\:\underset{\boldsymbol{{n}}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{\mathrm{1}}{\left(\mathrm{3}\boldsymbol{{n}}\right)!}=? \\ $$

Question Number 97963    Answers: 0   Comments: 0

Question Number 97956    Answers: 1   Comments: 0

prove Σ_(n=1) ^∞ ((9n+4)/(3n(3n+1)(3n+2)))=(3/2)−ln(3)

$${prove} \\ $$$$\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{\mathrm{9}{n}+\mathrm{4}}{\mathrm{3}{n}\left(\mathrm{3}{n}+\mathrm{1}\right)\left(\mathrm{3}{n}+\mathrm{2}\right)}=\frac{\mathrm{3}}{\mathrm{2}}−{ln}\left(\mathrm{3}\right) \\ $$

Question Number 97953    Answers: 1   Comments: 3

Question Number 97942    Answers: 2   Comments: 0

Question Number 97936    Answers: 1   Comments: 1

Find the value of (√(45−(√(2000)) )) + (√(45+(√(2000))))

$$\mathrm{Find}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\: \\ $$$$\sqrt{\mathrm{45}−\sqrt{\mathrm{2000}}\:}\:\:+\:\:\sqrt{\mathrm{45}+\sqrt{\mathrm{2000}}}\: \\ $$

Question Number 97929    Answers: 0   Comments: 1

Find equation of line through A(1,2,3) and parallel to y axis ?

$$\mathrm{Find}\:\mathrm{equation}\:\mathrm{of}\:\mathrm{line}\:\mathrm{through}\:\mathrm{A}\left(\mathrm{1},\mathrm{2},\mathrm{3}\right) \\ $$$$\mathrm{and}\:\mathrm{parallel}\:\mathrm{to}\:\mathrm{y}\:\mathrm{axis}\:?\: \\ $$

Question Number 97928    Answers: 1   Comments: 0

find the general formula ∫_0 ^(π/2) tan^α (x) dx

$${find}\:{the}\:{general}\:{formula} \\ $$$$\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} {tan}^{\alpha} \left({x}\right)\:{dx} \\ $$

Question Number 97922    Answers: 1   Comments: 0

y′′ + y = cot x

$$\mathrm{y}''\:+\:\mathrm{y}\:=\:\mathrm{cot}\:{x}\: \\ $$

Question Number 97918    Answers: 0   Comments: 1

Deleted one of the previous post. There is an option in app where you can use preferred font size. Soon another option will be added where you will able to use your preferred color combination.

$$\mathrm{Deleted}\:\mathrm{one}\:\mathrm{of}\:\mathrm{the}\:\mathrm{previous}\:\mathrm{post}.\: \\ $$$$\mathrm{There}\:\mathrm{is}\:\mathrm{an}\:\mathrm{option}\:\mathrm{in}\:\mathrm{app}\:\mathrm{where} \\ $$$$\mathrm{you}\:\mathrm{can}\:\mathrm{use}\:\mathrm{preferred}\:\mathrm{font}\:\mathrm{size}. \\ $$$$\mathrm{Soon}\:\mathrm{another}\:\mathrm{option}\:\mathrm{will}\:\mathrm{be}\:\mathrm{added} \\ $$$$\mathrm{where}\:\mathrm{you}\:\mathrm{will}\:\mathrm{able}\:\mathrm{to}\:\mathrm{use}\:\mathrm{your} \\ $$$$\mathrm{preferred}\:\mathrm{color}\:\mathrm{combination}. \\ $$

Question Number 97920    Answers: 0   Comments: 4

Question Number 97919    Answers: 1   Comments: 2

Question Number 97901    Answers: 2   Comments: 2

Question Number 97888    Answers: 1   Comments: 2

how to prove ((the volumn of dimensional sphare)) formula V_N (R)=(π^(N/2) /(Γ((N/2)+1))) R^N

$${how}\:{to}\:{prove}\:\left(\left({the}\:{volumn}\:{of}\right.\right. \\ $$$$\left.{d}\left.{imensional}\:{sphare}\right)\right)\:{formula} \\ $$$${V}_{{N}} \left({R}\right)=\frac{\pi^{{N}/\mathrm{2}} }{\Gamma\left(\frac{{N}}{\mathrm{2}}+\mathrm{1}\right)}\:{R}^{{N}} \\ $$$$ \\ $$

Question Number 97891    Answers: 0   Comments: 6

Question Number 97885    Answers: 2   Comments: 2

hello every one how do they calculated the universe old wich is 13.8 billion years

$${hello}\:{every}\:{one} \\ $$$${how}\:{do}\:{they}\:{calculated}\:{the}\:{universe}\:{old} \\ $$$${wich}\:{is}\:\mathrm{13}.\mathrm{8}\:{billion}\:{years} \\ $$

Question Number 97868    Answers: 2   Comments: 0

3y′ = 2x+y−1

$$\mathrm{3y}'\:=\:\mathrm{2x}+\mathrm{y}−\mathrm{1}\: \\ $$

Question Number 97866    Answers: 5   Comments: 4

Question Number 97858    Answers: 1   Comments: 1

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