Treatise on Trigonometry ...Macmillen & Company, 1889 - 504 sider |
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Side xv
... Convergent and Divergent . General theorems on convergency Theorems on alternately signed series Theorems on series of same sign throughout 439 442 . Limits . 443-445 . 446-448 . 449-457 . 458 , 459 . 460 462 . Principle of equating ...
... Convergent and Divergent . General theorems on convergency Theorems on alternately signed series Theorems on series of same sign throughout 439 442 . Limits . 443-445 . 446-448 . 449-457 . 458 , 459 . 460 462 . Principle of equating ...
Side 325
... convergent . DEF . 1. An endless series is said to be Convergent if there is some one finite quantity towards which the sum of its terms approximates , in such wise that by increasing the number of these terms we may make the difference ...
... convergent . DEF . 1. An endless series is said to be Convergent if there is some one finite quantity towards which the sum of its terms approximates , in such wise that by increasing the number of these terms we may make the difference ...
Side 327
... convergent or divergent . For if , for some forms of ƒ and 4 , the sum of ƒ ( r ) terms differs from that of ( r ) terms by a quantity whose limit — when r is co - is not zero , the series must be infinite for all values of n , when n ...
... convergent or divergent . For if , for some forms of ƒ and 4 , the sum of ƒ ( r ) terms differs from that of ( r ) terms by a quantity whose limit — when r is co - is not zero , the series must be infinite for all values of n , when n ...
Side 328
... convergent . 447. ( II . ) Hence , a series which is arranged in groups al- ternately signed will be finite for all values of n , if every group is arithmetically greater than the preceding but less than some finite quantity . For let ...
... convergent . 447. ( II . ) Hence , a series which is arranged in groups al- ternately signed will be finite for all values of n , if every group is arithmetically greater than the preceding but less than some finite quantity . For let ...
Side 329
... convergent , if the ratio of every term to the preceding is less than some quantity less than unity . Let Un + 1 < k where k < 1 . Then Un ( 1 − k ) ( U1 + U2 + U2 + ... ) = U1 − ku ̧ + u2 − ku2 + a finite series , by Art . 446 ...
... convergent , if the ratio of every term to the preceding is less than some quantity less than unity . Let Un + 1 < k where k < 1 . Then Un ( 1 − k ) ( U1 + U2 + U2 + ... ) = U1 − ku ̧ + u2 − ku2 + a finite series , by Art . 446 ...
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acute angle algebraically angle AOB antiparallel base bisector bisects Brocard Brocard Circle Brocard Points centre chord circular measure circumcircle circumference circumradius convergent cos² cos³ cosec cosh cosine cot² cotangent decimal diameter difference directed length equal equation escribed circles Example expressed factors figure final line finite formulæ greater Hence hypothenuse inscribed integral last article Lemoine Circle logarithms magnitude middle point multiple negative nine-points circle obtuse opposite perp perpendicular positive PROP prove quadrant quantity radian radii radius ratios respectively revolver right-angled triangle S₁ sec² secant sector sides sin² sin³ sine sinh subtend subtraction tan-¹ tan² tangent theorem trigonometrical angle values zero
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