 | George Chrystal - 1889 - 624 páginas
...(l±x)">l±?u:(a;<l and na positive integer). They are useful in the theory of infinite products. § 8.] The arithmetic mean of n positive quantities is not less than their geometric mean. Let us suppose this theorem to hold for n quantities a, b, e, . . ., k, and let I be... | |
 | University of Sydney - 1906 - 738 páginas
...X/y)=/[a+y), and deduce the exponential theorem. Prove that t* x «TX «T . . . . to 00= . 1 — x G. Prove that the arithmetic mean of n positive quantities is not less than their geometric mean. If j.\xt ....*„ and also Oja, ....«„ be positive quantities, prove that 2[a ]... | |
 | University of Calcutta - 1907 - 446 páginas
...a', B' of express 4 (a — a') (a — 0') (8 — o') (fl— B') in terms of p, q, p'. q'. 2. Prove that the arithmetic mean of n positive quantities is not less than their geometric mean. If *|. xn, arg. ... BII and also i/j, i;j, yg, ... ?/M be positive and in ascending... | |
 | University of Calcutta - 1914 - 822 páginas
...Candidates are permitted to attempt EIGHT questions only. The questions are all o/ equal value. 1. The arithmetic mean of n positive quantities is not less than their geometric mean. If f*+y*+z* + 2xyz=l. then will all or none of the quantities x, y, t, lie between... | |
 | University of Calcutta - 1916 - 802 páginas
...1111 (1) —+—+—+—+ ... ; \P 2" 3.'' 4" IP 3p 5f I Prove that the aeries n divergent. 3. Prove that the arithmetic mean of n positive quantities is not less than the geometric mean. Prove that (o + &+c)3>27 o6c<9 (а«+Ь»+с8). 4. Establish the law of the formation... | |
 | 1905 - 328 páginas
...Determination of the Radii of the Circles which touch Three given Circles. Mar. 10. Lindsay, WA — A Proof of the Theorem that the Arithmetic Mean of...Positive Quantities is not less than their Harmonic Mean [Title]. June 13. M.Intyre, JHA — On Mathematical Instruments and the Accuracy to be Obtained with... | |
 | George Chrystal - 1999 - 652 páginas
...(1±я)*>1±ад {»<! and na positive integer). They are useful in the theory of infinite products. § 8.] The arithmetic mean of n positive quantities is not less than their geometric mean. Let us suppose this theorem to hold for n quantities а, Ъ, с, . . ., k, and let... | |
 | Edinburgh Mathematical Society - 1903 - 540 páginas
...A. Determination of the radii of the circles which touch three given circles, - • - 75 LINDSAY, WA A Proof of the Theorem that the Arithmetic Mean of...positive quantities is not less than their Harmonic Mean [Title], 54 M'ISTYKE, JHA On Mathematical Instruments and the accuracy to be obtained with them in... | |
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Theorem that the Arithmetic Mean of n Positive Quantities is not less than their Harmonic Mean [Title]. 