 | Isaac Todhunter - 1870 - 818 pages
...contains the remaining things. Such combinations are called complementary. 496. To find for what value of r the number of combinations of n things taken r at a time is greatest. Let (та), denote the number of combinations of n things taken r at a time, (n)r... | |
 | Isaac Todhunter - Algebra - 1875 - 640 pages
...contains the remaining things. Such combinations are called complementary. 496. To find for what value of r the number of combinations of n things taken r at a time is greatest. Let (n)r denote the number of combinations of n things taken r at a time, (w)r_!... | |
 | James Edward Oliver - Trigonometry - 1881 - 140 pages
...cniSsin30cosn-30 •90] cos?i0 = cos"0— cnj2sin20cos"~204-cn,4sin40cosn~40— ; wherein cn_r denotes n(n — 1) (n — 2) (n — r + 1) 1.2.3 r the number of combinations...infinitesimal angle, then lim (sin0 : 0) = 1, and lim (tan 0 : 0) = 1. For, let c be the circumference of a circle, ^ , o the centre, p and p' the perimeters... | |
 | James Edward Oliver - Trigonometry - 1881 - 120 pages
...= cos"0 — Cn<2sin20cos"-20+c„<4sin40cosn-40 — ; wherein c^, denotes n(n -1) (n — 2) <ro — r + 1) 1.2.3 r the number of combinations of n things...DIFFERENTIATION OF TRIGONOMETRIC FUNCTIONS. LEMMA. If в be an infinitesimal angle, then lim (sino : в) =1, and lim (tano: 0) = 1. For, let c be the circumference... | |
 | James Edward Oliver - Trigonometry - 1889 - 178 pages
...sin2 в cos" 2 в + C4n si»4 0 cos" ~4 в — . . . ; wherein crn = n(n — 1) ... (n — r + 1) : r !, the number of combinations of n things taken r at a time. Eg, sin 30 = 3 sin0 cos20 — sin30 = 3sin0 — 4sin3Ö, cos Зв= cos3 в — 3 cos в sins... | |
 | 1879 - 636 pages
...0, when n is a positive integer and apply your method to cos5 0. III. — 1. Find for what value of r the number of combinations of n things taken r at a time is greatest. 2. Shew that an equation of the «'* degree cannot have more than n roots. 3. State... | |
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For, let c be the circumference of a circle, ^ , o the centre, p and p' the perimeters of two ^^ \ regular polygons of the same number of sides, the first inscribed in and the other circumscribed about the circle, and having their sides PP', TT', parallel... 