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Question Number 128256    Answers: 0   Comments: 6

1+(1/(2!1!))((1/2))^2 +(1/(3!2!))(((1.3)/2^2 ))^2 +(1/(4!3!))(((1.3.5)/2^3 ))^2 +....=(4/π) Prove the above Relation

1+12!1!(12)2+13!2!(1.322)2+14!3!(1.3.523)2+....=4πProvetheaboveRelation

Question Number 128236    Answers: 0   Comments: 1

(1/6)Σ_p ^∞ ((logp)/(p^2 −1))=((log1)/π^2 )+((log2)/(4π^2 ))+((log3)/(9π^2 ))+... (p=prime)

16plogpp21=log1π2+log24π2+log39π2+...(p=prime)

Question Number 128197    Answers: 1   Comments: 1

Question Number 128182    Answers: 1   Comments: 1

Question Number 128126    Answers: 1   Comments: 0

(4/(99)) + (7/(999)) + ((11)/(999999)) = ?

499+7999+11999999=?

Question Number 128122    Answers: 1   Comments: 0

1+(1/(16))+(5^2 /(16^2 .2!))+((5^2 .9^2 )/(16^3 .3!))+((5^2 .9^2 .13^2 )/(16^4 .4!))+...=((√π)/(Γ^2 ((3/4))))=F_1 ((1/4),(1/4),1;1) Prove The above relation Where F_1 (Φ,ϕ,γ;μ)=Σ_(n≥0) ^∞ (((Φ)_n (ϕ)_n )/(n!(γ)_n ))μ^n (ζ)_n =ζ(ζ+1)(ζ+2)...(ζ+n−1)

1+116+52162.2!+52.92163.3!+52.92.132164.4!+...=πΓ2(34)=F1(14,14,1;1)ProveTheaboverelationWhereF1(Φ,φ,γ;μ)=n0(Φ)n(φ)nn!(γ)nμn(ζ)n=ζ(ζ+1)(ζ+2)...(ζ+n1)

Question Number 128112    Answers: 3   Comments: 0

1 + 2 + 3 + 4 + ..... + 100 = ?

1+2+3+4+.....+100=?

Question Number 128110    Answers: 1   Comments: 0

∫_0 ^∞ ∫_0 ^∞ ((sinx sin(x+y))/(x(x+y)))dxdy

00sinxsin(x+y)x(x+y)dxdy

Question Number 128093    Answers: 1   Comments: 0

Question Number 128083    Answers: 2   Comments: 0

((8 − i)/(3 − 2i)) If the expression above is rewritten in the form a + bi, where a and b are real numbers, what is the value of a? A. 2 B. (8/3) C. 3 D. ((11)/3)

8i32iIftheexpressionaboveisrewrittenintheforma+bi,whereaandbarerealnumbers,whatisthevalueofa?A.2B.83C.3D.113

Question Number 128030    Answers: 1   Comments: 0

99 × 99 = 9801 999 × 999 = 998001 9999 × 9999 = 99980001 99999 × 99999 = ? 999999 × 999999 = ?

99×99=9801999×999=9980019999×9999=9998000199999×99999=?999999×999999=?

Question Number 128008    Answers: 1   Comments: 0

If 347.9823 = (3/P) + 4Q + 7R + (9/(10)) + (8/(100)) + (2/S) + (3/T) Then find the value of P + Q + R + S + T

If347.9823=3P+4Q+7R+910+8100+2S+3TThenfindthevalueofP+Q+R+S+T

Question Number 128001    Answers: 1   Comments: 0

(x − a) (x − b) (x − c) ..... (x − z) = ?

(xa)(xb)(xc).....(xz)=?

Question Number 127974    Answers: 1   Comments: 1

θ^(••) +(g/l)sinθ=0 Exact form (May include elliptic integral)

θ+glsinθ=0Exactform(Mayincludeellipticintegral)

Question Number 127970    Answers: 1   Comments: 0

You have given a positive integer N. Calculate ∫_( 0) ^( ∞) ((e^(2πx^2 ) − 1)/(e^(2πx^2 ) + 1))((1/x) − (x/(N^2 − x^2 ))) dx

YouhavegivenapositiveintegerN.Calculate0e2πx21e2πx2+1(1xxN2x2)dx

Question Number 127933    Answers: 1   Comments: 0

(1/((1/(x − 3)) + (1/(x + 4)))) If x > 0 and x ≠ 3, which of the following is equivalent to the expresion above? A. 2x + 1 B. x^2 + x − 12 C. ((x^2 + x − 12)/(2x + 1)) D. ((2x + 1)/(x^2 + x −12))

11x3+1x+4Ifx>0andx3,whichofthefollowingisequivalenttotheexpresionabove?A.2x+1B.x2+x12C.x2+x122x+1D.2x+1x2+x12

Question Number 127876    Answers: 0   Comments: 0

Consider the sequence defined by: 0<u_0 <1 and ∀n∈N, u_(n+1) =u_n −u_n ^2 . 1. Show that the sequence (u_n ) converges. What is its limit ? 2. Show that the series with general term u_n ^2 converges. 3. Show that the series with general terms ln((u_(n+1) /u_n )) and u_n diverge.

Considerthesequencedefinedby:0<u0<1andnN,un+1=unun2.1.Showthatthesequence(un)converges.Whatisitslimit?2.Showthattheserieswithgeneraltermun2converges.3.Showthattheserieswithgeneraltermsln(un+1un)andundiverge.

Question Number 127859    Answers: 1   Comments: 0

Question Number 127793    Answers: 2   Comments: 1

Σ_(n=1) ^∞ (n/(n!))cos(((πn)/5))

n=1nn!cos(πn5)

Question Number 127771    Answers: 0   Comments: 3

(1/(1−(π^2 /(1+π^2 −((2π^2 )/(2+π^2 −((3π^2 )/(3+π^2 −((4π^2 )/(4+π^2 −((5π^2 )/(5+π^2 ....))))))))))))

11π21+π22π22+π23π23+π24π24+π25π25+π2....

Question Number 127982    Answers: 0   Comments: 1

Some Values .. Σ_(n=−∞) ^∞ e^(−πn^2 ) =(π^(1/4) /(Γ((3/4)))) Σ_(n=−∞) ^∞ e^(−2πn^2 ) =(π^(1/4) /(Γ((3/4)))) (((6+4(√2)))^(1/4) /2) Σ_(n=−∞) ^∞ e^(−6πn^2 ) =(π^(1/4) /(Γ((3/4)))).((√((1)^(1/4) +(3)^(1/4) +(4)^(1/4) +(9)^(1/4) ))/( (√(1728)))) Any Idea to prove ?

SomeValues..n=eπn2=π14Γ(34)n=e2πn2=π14Γ(34)6+4242n=e6πn2=π14Γ(34).14+34+44+941728AnyIdeatoprove?

Question Number 127682    Answers: 1   Comments: 2

(π^2 /(1+(π^2 /(3−π^2 +((9π^2 )/(5−3π^2 +((25π^2 )/(7−5π^2 +((49π^( 2) )/(9−7π^2 +((81π^2 )/(11−9π^2 +((121π^2 )/(.....))))))))))))))

π21+π23π2+9π253π2+25π275π2+49π297π2+81π2119π2+121π2.....

Question Number 127666    Answers: 0   Comments: 11

Have a great year all of you It is 12.20 am in India (GMT+5.30) (12.20)^T =20.21 💐🌅

HaveagreatyearallofyouItis12.20aminIndia(GMT+5.30)(12.20)T=20.21💐🌅

Question Number 127644    Answers: 0   Comments: 2

(1/(1−(1/(2−((1/2)/((3/2)−((1/3)/((4/3)−((1/4)/((5/4)−((1/5)/((6/5)−...))))))))))))

11121232134314541565...

Question Number 127552    Answers: 0   Comments: 0

Question Number 127295    Answers: 0   Comments: 0

∫_0 ^(1/2) ((tanh^(−1) x)/( (x)^(1/5) ))dx

012tanh1xx5dx

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