Can someone solve this problem for me? Its about harmonic sequences.?
105928
Harmonic mean is the reciprocal of the mean of the reciprocals.\n\nLet the two number be a and b. The arithmetic mean of a and b is (a+b)/2 = 6, so a+b = 12. The harmonic mean of a and b is 2/(1/a+1/b) = 2ab/(a+b) = 9/2, so ab = 27. The sum of two numbers is 12 and the product is 27, so the two numbers are roots of x^2-12x+27 = 0, which can be factored into (x-3)(x-9) = 0. Therefore, the two numbers are 3 and 9.
286646
Try this: \nhttp://www.research.att.com/~njas/sequences/?q=3%2C3%2C4%2C5%2C7%2C8&sort=0&fmt=0&language=english&go=Search\n\nthere are several possible solutions, see what matches what you wanted
451479
hav u ever heard of the Principle of Mthematical Induction ?\nthat could solve ur problem in a jiffy!!\n\nHowever if u havn't, dont worry!!\n\nNote that, the sum in ur series(i.e. 1+1/2+1/3+...+1/n),where n>=2, is always less than 2, but greater than 1. so it can't b an integer.\nwanna know why?\ntry cramming up some theorems about Sequence & series of real numbers!! its a regulation part of any under-graduate level Real analysis course.
1130864
u(x, y) = e^(pi) e^x cos(ny)\n\nu_x (x, y) = e^(pi) e^x cos(ny)\n\nu_xx (x, y) = e^(pi) e^x cos(ny)     since e^(pi) cos(ny) is "constant" with respect to x\n\nu_y (x, y) = e^(pi) e^x (-nsin(ny))\n\nu_yy (x, y) = e^(pi) e^x (-n^2cos(ny))\n\nu_xx (x, y) + u_yy (x, y) = 0\n= e^(pi)(e^x)cos(ny)(1 - n^2)\n\nTherefore, u(x, y) is harmonic only if 1 - n^2 = 0, which is equivalent to n = 1 or n = -1.  For other values of n, we see that u(x, y) is, in general, not harmonic.\n\nTo find the harmonic conjugate v(x, y) of u(x, y) (for each of the cases n = 1 and n = -1), use the Cauchy-Riemann equations.\n\nThen use f(z) = f((z,0)) = u(z,0) + i v(z,0) to try to express w = u + iv in terms of z = x + iy (i.e. set y = 0 in u(x,y) and v(x,y), substitute into w = u(x, 0) + i v(x, 0)).
314821
It would be 622.5 Hz.\n\nThe second harmonic is twice the fundamental frequency, and the third harmonic is three times the fundamental frequency, so it would be 3/2 times the frequency of the second harmonic.
144611
You might find this paper useful\nhttp://arxiv.org/abs/math-ph/0106027
487838
1) Assuming an aritmetic sequence\n\nbn = b1 + (n-1)d \nletting b3=a1 = 20, then b7=a5 = 32, and b25 = b23\na5 = a1 + (5-1)d\n32 = 20 + (5-1)d\n32 = 20 + 4d\n12 = 4d\n3 = d\n\nb25 = a23 = 20 + (23-1)*3\nb25 = 20 + 22*3\nb25 = 20 + 66\nb25 = 86\n=====================================================\n2)\na75 = a1 + (75-1)d; d=-3\n\na75 = 5 + (75-1)*-3\na75 = 5 + 74*-3\na75 = 5 + -222\na75 = -217\n\nSn = n/2(a1+an)\nS75 = 75/2(5 + -217)\nS75 = 75/2(-212)\nS75 = -7950\n===================================================\n3) ????\n\na5 = 5*5 - 4 = 21\na15 = 5*15 - 4 = 71\na25 = 5*25 - 4 = 121\n\nOR MAYBE\n\na1 = 5*1 - 4\na1 = 5 - 4\na1 = 1\na30 = 5*30 - 4\na30 = 150 - 4\na30 = 146\n\nSn = n/2(a1+an)\nS30 = 30/2(1 + 146)\nS30 = 30/2(147)\nS30 = 2205\n================================================\n4)\n\nrth term is nCr-1m^n-(r-1)k^r-1\n\n5th term =\n4C4m^4-(5-1)k^5-1\n4C4 = 1\n\n5th term = k^4
765864
I'm unclear with the way you stated the problem. Am I looking for a implicit derivative. I'll check back to solve it.
669748
Just think a bit to locate the pattern by lookinh the first four terms.\nYou either get a common fifference or common ratio, ie you get AP or GP.\n\nIf the series is in fraction and above two does not comes, take reciprocal and see for common diffrence, Harmonic Pogression.\n\nIn word problem you have to figure out the pattern first, then apply formula...hope it helps!
475920
Homework?\n\nSuppose f is not identically 0. Then there is an interval where f stays away from 0. The g be the step function of this interval to get a contradiction.
844539
1. An arithmetic sequence has a(sub 5)= -10 and a(sub 12) =18. Find a(sub 2) and a(sub 17)\n\nLet a(sub 1) = a and d = common difference.\nFor an AP:\na(sub n) = a + (n - 1)d\n\nSo a(sub 5) = a + 4d = -10 .... (1)\nand a(sub12) = a + 11d = 18 . (2)\nEquation (2) - equuation (1)\n7d = 28\nSo d = 4\nSo a = -26\na(sub 2) = a + d = -22\na(sub 17) = a + 16d = 38\n\n2. Find s(sub 4) for the geomtric sequence: \na(sub 1) = 5p, a(sub 2) = -10p\n\nLet a(sub 1) = a and common ratio be r\n\nFor a GP\na(sub n) = ar^(n-1)\n\na(sub 1) = a = 5p .......... (1)\na(sub 2) = ar =  -10p ..... (2)\nEquation (2)/equation (1)\nr = -2\n\nSo a(sub n) = 5p * (-2)^(n-1)\n\ns(sub n) = a(r^n - 1)/(r - 1)\n= 5p((-2)^n) - 1)/(-2 - 1)\n= -5p/3 ((-2)^n - 1)\n\nSo s(sub 4) = -5p/3 ((-2)^4 - 1)\n= -25p
644170
The answer of "nayanmange" is right but his formula is wrong because it does not predict the sequence correctly. The correct formula is (2n-1)-th and 2n-th term of the series are {(2n-1)^2+1} and {(2n)^2-1} respectively. For n = 3 we find the (2*3)-th i.e. 6th term of the series as {(2*3)^2-1} = 35.
120241
You need to do a Poisson integral. Rather than try to write things out, I refer you to eqaution (3) on the mathworld site.\n\n\nhttp://mathworld.wolfram.com/PoissonIntegral.html\n\nI hope that helps.
1092202
looks like you've defined e using a series.  I think you need some periods of ellipsis to show that that series is infinite, since e is an irrational number
163726
It is Parseval's theorem you seek. "The total energy contained in a waveform x(t) summed across all of time t is equal to the total energy of the waveform's Fourier Transform X(f) summed across all of its frequency components f."\n\nFor a periodic signal, take the energy in each frequency for one period.  Sum those and you have the total energy.  The maximum amplitude during the period would be if all of that energy occured at once (i.e. an  impulse).  Convert that to dBm or DBW and you have your answer in dB.\n\nLook at the last equation in the link in "sources".
1089657
1)Linear Sequences : ex. a=2n , n>=1:\n1,2,4,8,16,32,...\n\n2)Quadratic Sequences : ex. a=n^2 , n>=2:\n4,9,16,25,36,49,64,81,....\n\n3)Cubic Sequences : ex. a=n^3 , n>=2:\n8,27,125,.....\n\n4)Polynomial Sequences : ex. a=2^n , n>=0:\n1,2,4,8,16,32,64,128,....\n\n5)Factorial Sequences : ex. a=n! , n>=0:\n1,1,2,6,24,120,....\n\nAll the above are devided into 2 major types : finite and infinite sequences...
883038
If you mean Hermite see\nhttp://mathworld.wolfram.com/HermiteDifferentialEquation.html