Question and Answers Forum

All Questions   Topic List

AllQuestion and Answers: Page 1631

Question Number 45364    Answers: 1   Comments: 0

Find the sum of n terms: (1/(1.3)) + (1/(3.5)) + ... + (1/((2n − 1)(2n + 1))) = ?

$$\mathrm{Find}\:\mathrm{the}\:\mathrm{sum}\:\mathrm{of}\:\mathrm{n}\:\mathrm{terms}:\:\:\frac{\mathrm{1}}{\mathrm{1}.\mathrm{3}}\:+\:\frac{\mathrm{1}}{\mathrm{3}.\mathrm{5}}\:+\:...\:+\:\frac{\mathrm{1}}{\left(\mathrm{2n}\:−\:\mathrm{1}\right)\left(\mathrm{2n}\:+\:\mathrm{1}\right)}\:\:=\:? \\ $$

Question Number 45356    Answers: 1   Comments: 0

x=(1/(1+(1/(2+(1/(3+(1/(4+...))))))))=?

$${x}=\frac{\mathrm{1}}{\mathrm{1}+\frac{\mathrm{1}}{\mathrm{2}+\frac{\mathrm{1}}{\mathrm{3}+\frac{\mathrm{1}}{\mathrm{4}+...}}}}=? \\ $$

Question Number 45353    Answers: 1   Comments: 3

Prove that p(n)=((a_1 +a_2 +...+a_n )/n) ≥^n (√(a_1 a_2 ...a_n )) ∀ n ∈N

$$\mathrm{Prove}\:\mathrm{that}\:\mathrm{p}\left(\mathrm{n}\right)=\frac{\boldsymbol{\mathrm{a}}_{\mathrm{1}} +\boldsymbol{\mathrm{a}}_{\mathrm{2}} +...+\boldsymbol{\mathrm{a}}_{\mathrm{n}} }{\mathrm{n}}\:\geqslant\:^{\mathrm{n}} \sqrt{\boldsymbol{\mathrm{a}}_{\mathrm{1}} \boldsymbol{\mathrm{a}}_{\mathrm{2}} ...\boldsymbol{\mathrm{a}}_{\boldsymbol{\mathrm{n}}} } \\ $$$$\forall\:\mathrm{n}\:\in\boldsymbol{\mathrm{N}} \\ $$

Question Number 45352    Answers: 1   Comments: 0

Question Number 45346    Answers: 1   Comments: 2

Question Number 45334    Answers: 1   Comments: 0

Question Number 45327    Answers: 2   Comments: 0

Question Number 45316    Answers: 1   Comments: 0

I heard this sum can be close using the Digamma function. Please help me use it. i don′t know it. sum of nth term: (1/(1.2.3)) + (1/(4.5.6)) + (1/(7.8.9)) + ...

$$\mathrm{I}\:\mathrm{heard}\:\mathrm{this}\:\mathrm{sum}\:\mathrm{can}\:\mathrm{be}\:\mathrm{close}\:\mathrm{using}\:\mathrm{the}\:\mathrm{Digamma}\:\mathrm{function}. \\ $$$$\mathrm{Please}\:\mathrm{help}\:\mathrm{me}\:\mathrm{use}\:\mathrm{it}.\:\mathrm{i}\:\mathrm{don}'\mathrm{t}\:\mathrm{know}\:\mathrm{it}.\:\:\: \\ $$$$\:\:\:\mathrm{sum}\:\mathrm{of}\:\mathrm{nth}\:\mathrm{term}:\:\:\:\frac{\mathrm{1}}{\mathrm{1}.\mathrm{2}.\mathrm{3}}\:+\:\frac{\mathrm{1}}{\mathrm{4}.\mathrm{5}.\mathrm{6}}\:+\:\frac{\mathrm{1}}{\mathrm{7}.\mathrm{8}.\mathrm{9}}\:+\:...\: \\ $$

Question Number 45314    Answers: 1   Comments: 0

solve for x 10^x =x^(50)

$$\boldsymbol{\mathrm{solve}}\:\boldsymbol{\mathrm{for}}\:\boldsymbol{{x}} \\ $$$$\mathrm{10}^{\boldsymbol{{x}}} =\boldsymbol{{x}}^{\mathrm{50}} \\ $$

Question Number 45313    Answers: 1   Comments: 1

Question Number 45291    Answers: 1   Comments: 0

How many possible triple of (a,b,c) ∈ integers so that : ∣ a + b ∣ + c = 19 ab + ∣ c ∣ = 97

$${How}\:\:{many}\:\:{possible}\:\:{triple}\:\:{of}\:\:\left({a},{b},{c}\right)\:\:\in\:\:{integers}\:\:{so}\:\:{that}\:\:: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\mid\:{a}\:+\:{b}\:\mid\:+\:{c}\:\:=\:\:\mathrm{19} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:{ab}\:+\:\mid\:{c}\:\mid\:\:=\:\:\mathrm{97} \\ $$

Question Number 45284    Answers: 1   Comments: 2

Question Number 45281    Answers: 1   Comments: 2

Question Number 45283    Answers: 1   Comments: 0

if x=1+a+a^2 +a^3 +……… y=1+b+b^2 +b^3 +……… prove that 1+ab+a^2 b^2 +a^3 b^3 +………=((xy)/(x+y−1))

$$\boldsymbol{\mathrm{if}}\:\boldsymbol{\mathrm{x}}=\mathrm{1}+\boldsymbol{\mathrm{a}}+\boldsymbol{\mathrm{a}}^{\mathrm{2}} +\boldsymbol{\mathrm{a}}^{\mathrm{3}} +\ldots\ldots\ldots \\ $$$$\:\:\:\:\boldsymbol{\mathrm{y}}=\mathrm{1}+\boldsymbol{\mathrm{b}}+\boldsymbol{\mathrm{b}}^{\mathrm{2}} +\boldsymbol{\mathrm{b}}^{\mathrm{3}} +\ldots\ldots\ldots \\ $$$$\boldsymbol{\mathrm{prove}}\:\boldsymbol{\mathrm{that}} \\ $$$$\mathrm{1}+\boldsymbol{\mathrm{ab}}+\boldsymbol{\mathrm{a}}^{\mathrm{2}} \boldsymbol{\mathrm{b}}^{\mathrm{2}} +\boldsymbol{\mathrm{a}}^{\mathrm{3}} \boldsymbol{\mathrm{b}}^{\mathrm{3}} +\ldots\ldots\ldots=\frac{\boldsymbol{\mathrm{xy}}}{\boldsymbol{\mathrm{x}}+\boldsymbol{\mathrm{y}}−\mathrm{1}} \\ $$

Question Number 45280    Answers: 2   Comments: 0

solve the simultaneous equation a)sin(x+y)=(1/((√2) )) cos2x=((-1 )/2) for x and y ranging from 0 to 360 inclusive b)if siny+cosx=x show that (d^2 y/dx^(2 ) ) =(x/((2−x^2 )^(3/2) ))

$$\boldsymbol{\mathrm{solve}}\:\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{simultaneous}}\:\boldsymbol{\mathrm{equation}} \\ $$$$\left.\boldsymbol{\mathrm{a}}\right)\boldsymbol{\mathrm{sin}}\left(\boldsymbol{\mathrm{x}}+\boldsymbol{\mathrm{y}}\right)=\frac{\mathrm{1}}{\sqrt{\mathrm{2}}\:\:\:} \\ $$$$\boldsymbol{\mathrm{cos}}\mathrm{2}\boldsymbol{\mathrm{x}}=\frac{-\mathrm{1}\:\:}{\mathrm{2}}\:\boldsymbol{\mathrm{for}}\:\boldsymbol{\mathrm{x}}\:\boldsymbol{\mathrm{and}}\:\boldsymbol{\mathrm{y}}\:\boldsymbol{\mathrm{ranging}}\:\boldsymbol{\mathrm{from}}\:\mathrm{0}\:\boldsymbol{\mathrm{to}}\:\mathrm{360}\:\boldsymbol{\mathrm{inclusive}} \\ $$$$\left.\boldsymbol{\mathrm{b}}\right)\boldsymbol{\mathrm{if}}\:\boldsymbol{\mathrm{siny}}+\boldsymbol{\mathrm{cosx}}=\boldsymbol{\mathrm{x}}\:\:\boldsymbol{\mathrm{show}}\:\boldsymbol{\mathrm{that}}\:\frac{\boldsymbol{\mathrm{d}}^{\mathrm{2}} \boldsymbol{\mathrm{y}}}{\boldsymbol{\mathrm{dx}}^{\mathrm{2}\:} }\:=\frac{\boldsymbol{\mathrm{x}}}{\left(\mathrm{2}−\boldsymbol{\mathrm{x}}^{\mathrm{2}} \right)^{\frac{\mathrm{3}}{\mathrm{2}}} } \\ $$

Question Number 45270    Answers: 2   Comments: 1

Question Number 45268    Answers: 0   Comments: 0

Question Number 45259    Answers: 2   Comments: 1

Find distance of point (1,1,1) from the line passing through (2,3,4) & (−1,2,3) ?

$${Find}\:\:{distance}\:{of}\:{point}\:\left(\mathrm{1},\mathrm{1},\mathrm{1}\right)\:{from} \\ $$$${the}\:{line}\:{passing}\:{through}\:\left(\mathrm{2},\mathrm{3},\mathrm{4}\right)\:\& \\ $$$$\left(−\mathrm{1},\mathrm{2},\mathrm{3}\right)\:? \\ $$

Question Number 45264    Answers: 0   Comments: 4

Question Number 45239    Answers: 0   Comments: 0

find the range of the following (i) f(x)=arcsin(x) (ii)f(x)=arccos(x) (iii)f(x)=arctan(x)

$$\boldsymbol{\mathrm{find}}\:\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{range}}\:\boldsymbol{\mathrm{of}}\:\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{following}} \\ $$$$\left(\boldsymbol{\mathrm{i}}\right)\:\boldsymbol{\mathrm{f}}\left(\boldsymbol{{x}}\right)=\boldsymbol{\mathrm{arcsin}}\left(\boldsymbol{{x}}\right) \\ $$$$\left(\boldsymbol{\mathrm{ii}}\right)\boldsymbol{\mathrm{f}}\left(\boldsymbol{{x}}\right)=\boldsymbol{\mathrm{arccos}}\left(\boldsymbol{{x}}\right) \\ $$$$\left(\boldsymbol{\mathrm{iii}}\right)\boldsymbol{\mathrm{f}}\left(\boldsymbol{{x}}\right)=\boldsymbol{\mathrm{arctan}}\left(\boldsymbol{{x}}\right) \\ $$

Question Number 45240    Answers: 2   Comments: 1

calculate Σ_(n=2) ^∞ ((2n+1)/(n^4 −n^2 ))

$${calculate}\:\sum_{{n}=\mathrm{2}} ^{\infty} \:\:\frac{\mathrm{2}{n}+\mathrm{1}}{{n}^{\mathrm{4}} −{n}^{\mathrm{2}} } \\ $$

Question Number 45237    Answers: 1   Comments: 1

calculate Σ_(n=2) ^∞ (1/(n^3 −n))

$${calculate}\:\sum_{{n}=\mathrm{2}} ^{\infty} \:\frac{\mathrm{1}}{{n}^{\mathrm{3}} −{n}} \\ $$

Question Number 45235    Answers: 0   Comments: 2

let ∣a∣<1 and f(a)=∫_0 ^1 ln(x)ln(1+ax)dx 1) find a explicit form of f(a) 2) calculate g(a) =∫_0 ^1 ((xln(x))/(1+ax))dx 3) calculate ∫_0 ^1 ln(x)ln(2+x)dx 4) calculate ∫_0 ^1 ((xln(x))/(2+x))dx 5) calculate u_n =∫_0 ^1 ((xln(x))/(n+x))dx with n integr and n>1 find nature of the serie Σ u_n

$${let}\:\mid{a}\mid<\mathrm{1}\:{and}\:\:{f}\left({a}\right)=\int_{\mathrm{0}} ^{\mathrm{1}} {ln}\left({x}\right){ln}\left(\mathrm{1}+{ax}\right){dx} \\ $$$$\left.\mathrm{1}\right)\:{find}\:{a}\:{explicit}\:{form}\:{of}\:{f}\left({a}\right) \\ $$$$\left.\mathrm{2}\right)\:{calculate}\:\:{g}\left({a}\right)\:=\int_{\mathrm{0}} ^{\mathrm{1}} \:\:\frac{{xln}\left({x}\right)}{\mathrm{1}+{ax}}{dx} \\ $$$$\left.\mathrm{3}\right)\:{calculate}\:\int_{\mathrm{0}} ^{\mathrm{1}} {ln}\left({x}\right){ln}\left(\mathrm{2}+{x}\right){dx} \\ $$$$\left.\mathrm{4}\right)\:{calculate}\:\int_{\mathrm{0}} ^{\mathrm{1}} \:\:\:\frac{{xln}\left({x}\right)}{\mathrm{2}+{x}}{dx}\: \\ $$$$\left.\mathrm{5}\right)\:{calculate}\:{u}_{{n}} =\int_{\mathrm{0}} ^{\mathrm{1}} \:\:\frac{{xln}\left({x}\right)}{{n}+{x}}{dx}\:{with}\:{n}\:{integr}\:{and}\:{n}>\mathrm{1} \\ $$$${find}\:{nature}\:{of}\:{the}\:{serie}\:\Sigma\:{u}_{{n}} \\ $$

Question Number 45213    Answers: 3   Comments: 0

Find ∫(√(a^2 −tan^2 x)) dx (with a>0) (related to Q45187)

$${Find}\:\int\sqrt{{a}^{\mathrm{2}} −\mathrm{tan}^{\mathrm{2}} \:{x}}\:{dx}\:\left({with}\:{a}>\mathrm{0}\right) \\ $$$$\left({related}\:{to}\:{Q}\mathrm{45187}\right) \\ $$

Question Number 45211    Answers: 1   Comments: 0

Let A= (((1 3)),((2 5)) ). Find an expression for the enteries of A^n .

$$\mathrm{Let}\:\mathrm{A}=\begin{pmatrix}{\mathrm{1}\:\:\:\:\:\mathrm{3}}\\{\mathrm{2}\:\:\:\:\:\mathrm{5}}\end{pmatrix}.\:\mathrm{Find}\:\mathrm{an}\:\mathrm{expression}\: \\ $$$$\mathrm{for}\:\mathrm{the}\:\mathrm{enteries}\:\mathrm{of}\:\mathrm{A}^{\mathrm{n}} . \\ $$

Question Number 45208    Answers: 0   Comments: 1

  Pg 1626      Pg 1627      Pg 1628      Pg 1629      Pg 1630      Pg 1631      Pg 1632      Pg 1633      Pg 1634      Pg 1635   

Terms of Service

Privacy Policy

Contact: info@tinkutara.com