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Question Number 35041 Answers: 0 Comments: 1

find the value of Σ_(n=1) ^∞ ((n+1)/(n^3 (n+1)^2 ))

$${find}\:{the}\:{value}\:{of}\:\:\sum_{{n}=\mathrm{1}} ^{\infty} \:\:\frac{{n}+\mathrm{1}}{{n}^{\mathrm{3}} \left({n}+\mathrm{1}\right)^{\mathrm{2}} } \\ $$

Question Number 35040 Answers: 0 Comments: 0

find the value of Σ_(n=1) ^∞ (x^n /(n(n+1)(2n−1))) 2) find the value of Σ_(n=1) ^∞ (((−1)^n )/(2^n n(n+1)(2n−1)))

$${find}\:{the}\:{value}\:{of}\:\sum_{{n}=\mathrm{1}} ^{\infty} \:\:\:\:\:\frac{{x}^{{n}} }{{n}\left({n}+\mathrm{1}\right)\left(\mathrm{2}{n}−\mathrm{1}\right)} \\ $$$$\left.\mathrm{2}\right)\:{find}\:{the}\:{value}\:{of}\:\:\sum_{{n}=\mathrm{1}} ^{\infty} \:\:\:\:\frac{\left(−\mathrm{1}\right)^{{n}} }{\mathrm{2}^{{n}} {n}\left({n}+\mathrm{1}\right)\left(\mathrm{2}{n}−\mathrm{1}\right)} \\ $$

Question Number 35023 Answers: 1 Comments: 1

Question Number 35021 Answers: 0 Comments: 1

Find the points at which the given function is discontinuous : f(x)= ∣x∣ sgn (x^3 −x) .

$${Find}\:{the}\:{points}\:{at}\:{which}\:{the}\:{given} \\ $$$${function}\:{is}\:{discontinuous}\:: \\ $$$${f}\left({x}\right)=\:\mid{x}\mid\:{sgn}\:\left({x}^{\mathrm{3}} −{x}\right)\:. \\ $$

Question Number 35018 Answers: 1 Comments: 0

∫∫∫((dxdydz)/((x+y+z+1)^3 )) bounded by the coordinate planes and the plane x+y+z=1 .

$$\int\int\int\frac{{dxdydz}}{\left({x}+{y}+{z}+\mathrm{1}\right)^{\mathrm{3}} }\:\:\:{bounded}\:{by}\:{the} \\ $$$${coordinate}\:{planes}\:{and}\:{the}\:{plane} \\ $$$${x}+{y}+{z}=\mathrm{1}\:. \\ $$

Question Number 35015 Answers: 2 Comments: 0

∫(x^2 /((1+x^3 )^2 ))dx

$$\int\frac{{x}^{\mathrm{2}} }{\left(\mathrm{1}+{x}^{\mathrm{3}} \right)^{\mathrm{2}} }{dx} \\ $$

Question Number 35005 Answers: 2 Comments: 0

Find remainder when 1!+2!+3!+...+99!+100! is divided by 12.

$$\mathrm{Find}\:\mathrm{remainder}\:\mathrm{when} \\ $$$$\:\:\:\:\mathrm{1}!+\mathrm{2}!+\mathrm{3}!+...+\mathrm{99}!+\mathrm{100}! \\ $$$$\mathrm{is}\:\mathrm{divided}\:\mathrm{by}\:\:\mathrm{12}. \\ $$

Question Number 35004 Answers: 3 Comments: 0

Prove that 41 divides 2^(20) −1

$$\mathrm{Prove}\:\mathrm{that}\:\mathrm{41}\:\mathrm{divides}\:\mathrm{2}^{\mathrm{20}} −\mathrm{1} \\ $$

Question Number 34992 Answers: 1 Comments: 1

∫_0 ^π ((cos(x))/(1+2sin(2x)))dx

$$\:\underset{\mathrm{0}} {\overset{\pi} {\int}}\frac{\mathrm{cos}\left({x}\right)}{\mathrm{1}+\mathrm{2sin}\left(\mathrm{2}{x}\right)}{dx} \\ $$

Question Number 34988 Answers: 1 Comments: 1

Question Number 34982 Answers: 2 Comments: 2

lim_(x→1) ((nx^(n+1) −(n+1)x^n +1)/((e^x −e)sin πx)) = ?

$$\underset{{x}\rightarrow\mathrm{1}} {\mathrm{lim}}\:\frac{{nx}^{{n}+\mathrm{1}} −\left({n}+\mathrm{1}\right){x}^{{n}} +\mathrm{1}}{\left({e}^{{x}} −{e}\right)\mathrm{sin}\:\pi{x}}\:=\:? \\ $$

Question Number 34980 Answers: 2 Comments: 0

If cos45° =(1/(√2)) . Find cos45.1°

$${If}\:{cos}\mathrm{45}°\:=\frac{\mathrm{1}}{\sqrt{\mathrm{2}}}\:.\:{Find}\:{cos}\mathrm{45}.\mathrm{1}° \\ $$

Question Number 34956 Answers: 3 Comments: 2

Question Number 34954 Answers: 1 Comments: 1

Question Number 34952 Answers: 0 Comments: 2

Question Number 34951 Answers: 1 Comments: 0

lim_(n→∞) (((e×a)/n))^n = ? Here aε R^+

$$\underset{{n}\rightarrow\infty} {\mathrm{lim}}\:\left(\frac{{e}×{a}}{{n}}\right)^{{n}} \:=\:?\: \\ $$$${Here}\:{a}\epsilon\:\mathbb{R}^{+} \\ $$

Question Number 34930 Answers: 1 Comments: 3

A committee of 4 is to be formed from 4 principals and 5 students.In how many ways can this be done if a particular student and a principal must be in the committee.

$${A}\:{committee}\:{of}\:\mathrm{4}\:{is}\:{to}\:{be}\:{formed} \\ $$$${from}\:\mathrm{4}\:{principals} \\ $$$${and}\:\mathrm{5}\:{students}.{In}\:{how}\:{many}\:{ways} \\ $$$${can}\:{this}\:{be}\:{done}\:{if}\:{a}\:{particular} \\ $$$${student}\:{and}\:{a}\:{principal}\:{must}\:{be} \\ $$$${in}\:{the}\:{committee}. \\ $$$$ \\ $$

Question Number 34921 Answers: 1 Comments: 0

lim_(x→∞) { (x/(x+(((x)^(1/3) )/(x+ (((x)^(1/3) )/(x+(((x)^(1/3) )/(......... infinity ))))))))}

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

Question Number 34913 Answers: 0 Comments: 6

let f(x)= (3/(2+cosx)) developp f ar fourier serie.

$${let}\:{f}\left({x}\right)=\:\frac{\mathrm{3}}{\mathrm{2}+{cosx}}\:\:{developp}\:{f}\:{ar}\:{fourier}\:{serie}. \\ $$

Question Number 34912 Answers: 1 Comments: 0

let f(x,y,z) =(x^2 +y^2 +z^2 )^α with α∈R 1) calculate Δf 2) find α in order to have Δf=0

$${let}\:{f}\left({x},{y},{z}\right)\:=\left({x}^{\mathrm{2}} \:+{y}^{\mathrm{2}} +{z}^{\mathrm{2}} \right)^{\alpha} \:\:\:\:\:{with}\:\alpha\in{R} \\ $$$$\left.\mathrm{1}\right)\:{calculate}\:\Delta{f} \\ $$$$\left.\mathrm{2}\right)\:{find}\:\alpha\:{in}\:{order}\:{to}\:{have}\:\Delta{f}=\mathrm{0} \\ $$

Question Number 34911 Answers: 1 Comments: 1

find ∫_2 ^3 ((2x^2 +3)/((x−1)^2 (x^2 +1))) dx

$${find}\:\:\:\int_{\mathrm{2}} ^{\mathrm{3}} \:\:\:\:\frac{\mathrm{2}{x}^{\mathrm{2}} \:+\mathrm{3}}{\left({x}−\mathrm{1}\right)^{\mathrm{2}} \left({x}^{\mathrm{2}} +\mathrm{1}\right)}\:{dx} \\ $$

Question Number 34910 Answers: 0 Comments: 1

find J_(n,p) =∫_0 ^∞ x^n e^(−(x^2 /p)) dx with p>0 and n integr

$${find}\:{J}_{{n},{p}} \:=\int_{\mathrm{0}} ^{\infty} \:\:{x}^{{n}} \:\:{e}^{−\frac{{x}^{\mathrm{2}} }{{p}}} \:\:{dx}\:\:{with}\:{p}>\mathrm{0}\:{and}\:{n}\:{integr} \\ $$

Question Number 35037 Answers: 0 Comments: 0

prove that ∀ n∈N Σ_(k=0) ^(2n) (−1)^k ( C_(2n) ^k )^2 =(−1)^n C_(2n) ^n .

$${prove}\:{that}\:\forall\:{n}\in{N} \\ $$$$\sum_{{k}=\mathrm{0}} ^{\mathrm{2}{n}} \:\left(−\mathrm{1}\right)^{{k}} \left(\:{C}_{\mathrm{2}{n}} ^{{k}} \right)^{\mathrm{2}} \:=\left(−\mathrm{1}\right)^{{n}} \:{C}_{\mathrm{2}{n}} ^{{n}} \:\:. \\ $$

Question Number 35036 Answers: 1 Comments: 0

cslculate Σ_(k=1) ^n k^2 (n+1−k)

$${cslculate}\:\sum_{{k}=\mathrm{1}} ^{{n}} {k}^{\mathrm{2}} \left({n}+\mathrm{1}−{k}\right) \\ $$

Question Number 35035 Answers: 1 Comments: 0

calculate u_n = Σ_(k=1) ^n (k/((k+1)!))

$${calculate}\:{u}_{{n}} =\:\sum_{{k}=\mathrm{1}} ^{{n}} \:\:\frac{{k}}{\left({k}+\mathrm{1}\right)!} \\ $$

Question Number 35032 Answers: 0 Comments: 0

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