A Treatise on the Calculus of Finite Differences |
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Page 65
... convergent or divergent accord- ing as the sum of its first n terms approaches or does not approach to a finite limit when n is indefinitely increased . This definition leads us to distinguish between the con- vergency of a series and ...
... convergent or divergent accord- ing as the sum of its first n terms approaches or does not approach to a finite limit when n is indefinitely increased . This definition leads us to distinguish between the con- vergency of a series and ...
Page 66
... convergent . uz Ex . Thus the series 1 -1 + 1 3 - 1 1 + 十 4 5 - & c . ad inf . tends to a limit which is less than 1 and greater than 1 3. The theory of the convergency and divergency of series whose terms are ultimately of one sign ...
... convergent . uz Ex . Thus the series 1 -1 + 1 3 - 1 1 + 十 4 5 - & c . ad inf . tends to a limit which is less than 1 and greater than 1 3. The theory of the convergency and divergency of series whose terms are ultimately of one sign ...
Page 67
George Boole .00 will be convergent or divergent according as [ * Þ ( x ) dæ is finite or infinite . a For since ( x ) diminishes from xa to x = a + 1 , and again from x = a + 1 to x = a + 2 , & c . , we have ra + 1 fa α ra + 2 4 $ ( x ) ...
George Boole .00 will be convergent or divergent according as [ * Þ ( x ) dæ is finite or infinite . a For since ( x ) diminishes from xa to x = a + 1 , and again from x = a + 1 to x = a + 2 , & c . , we have ra + 1 fa α ra + 2 4 $ ( x ) ...
Page 68
... convergent if h < 1 , divergent if h х 1 . The general term is h " , the value of x in the first term being 0 , so that the test of convergency is simply whether h * dx is infinite . Now hdx = hx 1 log h - · If h > 1 this expression ...
... convergent if h < 1 , divergent if h х 1 . The general term is h " , the value of x in the first term being 0 , so that the test of convergency is simply whether h * dx is infinite . Now hdx = hx 1 log h - · If h > 1 this expression ...
Page 69
... convergent or divergent according as the ratio tends , when x is indefinitely increased , to a limiting Ux + 1 Их value less or greater than unity . Let h be that limiting value ; and first let h be less than 1 , and let k be some ...
... convergent or divergent according as the ratio tends , when x is indefinitely increased , to a limiting Ux + 1 Их value less or greater than unity . Let h be that limiting value ; and first let h be less than 1 , and let k be some ...
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Common terms and phrases
A₁ A³u algebraic applying arbitrary constant ascending powers assume ax+b B₁ c₂ Calculus of Finite Cambridge CHARLES KINGSLEY cloth CO.'S PUBLICATIONS complete primitive CONIC SECTIONS convergent Crown 8vo curve deduce denoted determine Differential Calculus differential equation divergent English Notes equation of differences expression Fcap Fellow of St Finite Differences functional equation GEORGE BOOLE given equation Hence independent variable indirect integral John's College limit linear equation M.A. Second Edition MACMILLAN & CO.'S method mixed differences operation ordinates P. G. TAIT particular value periodical function rational and integral reduced result Schools second member Sermons shew singular solution substituting successive values supposed symbol theorem tion TODHUNTER Treatise Trinity College u₁ u₂ unity University of Cambridge Ux+1 Ux+2 v₂ Vx+1 Vx+2 whence Их
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