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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 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 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 45204    Answers: 0   Comments: 2

Question Number 45166    Answers: 1   Comments: 0

Question Number 45029    Answers: 0   Comments: 0

x^2 =12y

$$\mathrm{x}^{\mathrm{2}} =\mathrm{12y} \\ $$

Question Number 45014    Answers: 1   Comments: 6

6÷2(1+2)? which ans is correct between 1or 9 why do i look at the mobile phone calculator is 9 and when i check to scientific calculator the ans is 1.i want to clarify correctly where you are.

$$\mathrm{6}\boldsymbol{\div}\mathrm{2}\left(\mathrm{1}+\mathrm{2}\right)?\:\mathrm{which}\:\boldsymbol{\mathrm{ans}}\:\boldsymbol{\mathrm{is}}\:\boldsymbol{\mathrm{correct}}\:\boldsymbol{\mathrm{between}}\:\mathrm{1}\boldsymbol{\mathrm{or}}\:\mathrm{9} \\ $$$$\boldsymbol{\mathrm{why}}\:\boldsymbol{\mathrm{do}}\:\boldsymbol{\mathrm{i}}\:\boldsymbol{\mathrm{look}}\:\boldsymbol{\mathrm{at}}\:\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{mobile}}\:\boldsymbol{\mathrm{phone}}\:\boldsymbol{\mathrm{calculator}}\:\boldsymbol{\mathrm{is}}\:\mathrm{9}\:\boldsymbol{\mathrm{and}}\:\boldsymbol{\mathrm{when}}\:\boldsymbol{\mathrm{i}}\:\boldsymbol{\mathrm{check}}\:\boldsymbol{\mathrm{to}}\:\boldsymbol{\mathrm{scientific}}\:\boldsymbol{\mathrm{calculator}}\:\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{ans}}\:\boldsymbol{\mathrm{is}}\:\mathrm{1}.\boldsymbol{\mathrm{i}}\:\boldsymbol{\mathrm{want}}\:\boldsymbol{\mathrm{to}}\:\boldsymbol{\mathrm{clarify}}\:\boldsymbol{\mathrm{correctly}}\:\boldsymbol{\mathrm{where}}\:\boldsymbol{\mathrm{you}}\:\boldsymbol{\mathrm{are}}. \\ $$

Question Number 44965    Answers: 0   Comments: 0

Find the sum of the nth term of the series: (1/(1.2.3)) + (1/(4.5.6)) + (1/(7.8.9)) + ...

$$\mathrm{Find}\:\mathrm{the}\:\mathrm{sum}\:\mathrm{of}\:\mathrm{the}\:\mathrm{nth}\:\mathrm{term}\:\mathrm{of}\:\mathrm{the}\:\mathrm{series}:\:\:\:\:\frac{\mathrm{1}}{\mathrm{1}.\mathrm{2}.\mathrm{3}}\:+\:\frac{\mathrm{1}}{\mathrm{4}.\mathrm{5}.\mathrm{6}}\:+\:\frac{\mathrm{1}}{\mathrm{7}.\mathrm{8}.\mathrm{9}}\:\:+\:...\: \\ $$

Question Number 44936    Answers: 0   Comments: 0

Question Number 44918    Answers: 2   Comments: 5

Find the sum to n terms of: (1/(1.2.3)) + (3/(2.3.4)) + (5/(3.4.5)) + ...

$$\mathrm{Find}\:\mathrm{the}\:\mathrm{sum}\:\mathrm{to}\:\mathrm{n}\:\mathrm{terms}\:\mathrm{of}:\:\:\:\:\frac{\mathrm{1}}{\mathrm{1}.\mathrm{2}.\mathrm{3}}\:+\:\frac{\mathrm{3}}{\mathrm{2}.\mathrm{3}.\mathrm{4}}\:+\:\frac{\mathrm{5}}{\mathrm{3}.\mathrm{4}.\mathrm{5}}\:+\:...\: \\ $$

Question Number 44898    Answers: 1   Comments: 1

If x^4 +px^3 +qx^2 +rx+5 = 0 has four real roots, then find the minimum value of pr.

$${If}\:\:\:\:{x}^{\mathrm{4}} +{px}^{\mathrm{3}} +{qx}^{\mathrm{2}} +{rx}+\mathrm{5}\:=\:\mathrm{0} \\ $$$${has}\:{four}\:{real}\:{roots},\:{then}\:{find} \\ $$$$\:{the}\:{minimum}\:{value}\:{of}\:\boldsymbol{{pr}}. \\ $$

Question Number 44892    Answers: 1   Comments: 2

Find the formular for the sum of the first kth power of natural number

$$\mathrm{Find}\:\mathrm{the}\:\mathrm{formular}\:\mathrm{for}\:\mathrm{the}\:\mathrm{sum}\:\mathrm{of}\:\mathrm{the}\:\mathrm{first}\:\mathrm{kth}\:\mathrm{power}\:\mathrm{of}\:\mathrm{natural}\:\mathrm{number} \\ $$

Question Number 44876    Answers: 1   Comments: 0

Question Number 44819    Answers: 0   Comments: 7

Question Number 44783    Answers: 1   Comments: 0

(x^2 )^2 +(y^2 )^2 =97.......1 (x^2 )^3 +(y^2 )^3 =793.......2 solve the simultaneous equation

$$\left({x}^{\mathrm{2}} \right)^{\mathrm{2}} +\left({y}^{\mathrm{2}} \right)^{\mathrm{2}} =\mathrm{97}.......\mathrm{1} \\ $$$$\left({x}^{\mathrm{2}} \right)^{\mathrm{3}} +\left({y}^{\mathrm{2}} \right)^{\mathrm{3}} =\mathrm{793}.......\mathrm{2} \\ $$$${solve}\:{the}\:{simultaneous}\:{equation} \\ $$

Question Number 44773    Answers: 0   Comments: 0

$$ \\ $$

Question Number 44765    Answers: 0   Comments: 0

Question Number 44763    Answers: 1   Comments: 1

Question Number 44729    Answers: 4   Comments: 0

Question Number 44691    Answers: 1   Comments: 1

Question Number 44570    Answers: 1   Comments: 0

Question Number 44543    Answers: 1   Comments: 3

If y =f(x) = ax^2 +bx+c and at some x, say x= p ∫_0 ^( p) ydx = y(p)= y ′(p) = y ′′(p)= p , then find p .

$${If}\:\:{y}\:={f}\left({x}\right)\:=\:{ax}^{\mathrm{2}} +{bx}+{c} \\ $$$${and}\:\:{at}\:{some}\:{x},\:{say}\:\:{x}=\:{p} \\ $$$$\int_{\mathrm{0}} ^{\:\:{p}} {ydx}\:=\:{y}\left({p}\right)=\:{y}\:'\left({p}\right)\:=\:{y}\:''\left({p}\right)=\:{p}\:, \\ $$$${then}\:{find}\:\boldsymbol{{p}}\:. \\ $$

Question Number 44502    Answers: 1   Comments: 0

If a>b,and c>d,prove that a−c may be greater than, equal to or less than b−d.

$$\mathrm{If}\:\mathrm{a}>\mathrm{b},\mathrm{and}\:\mathrm{c}>\mathrm{d},\mathrm{prove}\:\mathrm{that}\:\mathrm{a}−\mathrm{c}\:\mathrm{may}\:\mathrm{be}\:\mathrm{greater}\:\mathrm{than}, \\ $$$$\mathrm{equal}\:\mathrm{to}\:\mathrm{or}\:\mathrm{less}\:\mathrm{than}\:\mathrm{b}−\mathrm{d}. \\ $$$$ \\ $$

Question Number 44444    Answers: 1   Comments: 0

simplify (√((4x^2 y)^(2/3) +(8x^2 y^2 )^4 ))

$${simplify}\:\:\:\:\sqrt{\left(\mathrm{4}{x}^{\mathrm{2}} {y}\right)^{\frac{\mathrm{2}}{\mathrm{3}}} +\left(\mathrm{8}{x}^{\mathrm{2}} {y}^{\mathrm{2}} \right)^{\mathrm{4}} } \\ $$

Question Number 44397    Answers: 2   Comments: 4

If x is nearly equal to 1 then ((mx^m −nx^n )/(m−n))=

$${If}\:{x}\:{is}\:{nearly}\:{equal}\:{to}\:\mathrm{1}\:{then} \\ $$$$\frac{{mx}^{{m}} −{nx}^{{n}} }{{m}−{n}}= \\ $$

Question Number 44384    Answers: 2   Comments: 6

Let a and b are real numbers such that a > b > 0 Find the minimum value of (√2)a^3 + (3/(ab − b^2 ))

$$\mathrm{Let}\:{a}\:\mathrm{and}\:{b}\:\mathrm{are}\:\mathrm{real}\:\mathrm{numbers}\:\mathrm{such}\:\mathrm{that} \\ $$$${a}\:>\:{b}\:>\:\mathrm{0} \\ $$$$\mathrm{Find}\:\mathrm{the}\:\mathrm{minimum}\:\mathrm{value}\:\mathrm{of} \\ $$$$\sqrt{\mathrm{2}}{a}^{\mathrm{3}} \:+\:\frac{\mathrm{3}}{{ab}\:−\:{b}^{\mathrm{2}} } \\ $$

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