Advanced Course in Algebra
Advanced Course in Algebra
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In our eReader you can find the full English version of the book. Read Advanced Course in Algebra Online - link to read the book on full screen. Our eReader also allows you to upload and read Pdf, Txt, ePub and fb2 books. In the Mini eReder on the page below you can quickly view all pages of the book - Read Book Advanced Course in Algebra
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||, ±, ... to 6 terms.
6. ||, 2, ... to 7 terms. 9. - i, |, - 1 , to 8 terma.
529. If any three of the five elements of a geometric pro- gression are given, the other two may be found by substituting the given values in the fundamental formulas (I) and (II), and solving the resulting equations.
But in certain cases the operation involves the solution of an equation of a degree higher than the second; and in others the unknown number appears as an exponent, the solution of which form of equation... can usually only be affected by the aid of logarithms (§ 604).
In all such cases in the present chapter, the equations may be solved by inspection.
1. Given a = — 2, n = 5, Z = — 32 ; find r and S.
Substituting the given values in (I), we have — 32 = — 2r*; whence, r* = 16, or r=±2.
Substituting in (II), If r= 2, ;S = ^(~^5~/~^) = -64 + 2 = -62.
n r = -2, g = (-^)(-32)-(^2)^64 + 2^^^^ * ' -2-1 -3 The solution is, r = 2, /S = — 62; or, r = — 2, /S = — 22.
The significanoe of the two answers is as follows : If r= 2, the progression 18—2, —4, —8, —16, —82, whose som is —02.
What to read after Advanced Course in Algebra?
You can find similar books in the "Read Also" column, or choose other free books by Webster Wells to read onlineMoreLess
To quickly assess the difficulty of the text, read a short excerpt:
||, ±, ... to 6 terms.
6. ||, 2, ... to 7 terms. 9. - i, |, - 1 , to 8 terma.
529. If any three of the five elements of a geometric pro- gression are given, the other two may be found by substituting the given values in the fundamental formulas (I) and (II), and solving the resulting equations.
But in certain cases the operation involves the solution of an equation of a degree higher than the second; and in others the unknown number appears as an exponent, the solution of which form of equation... can usually only be affected by the aid of logarithms (§ 604).
In all such cases in the present chapter, the equations may be solved by inspection.
1. Given a = — 2, n = 5, Z = — 32 ; find r and S.
Substituting the given values in (I), we have — 32 = — 2r*; whence, r* = 16, or r=±2.
Substituting in (II), If r= 2, ;S = ^(~^5~/~^) = -64 + 2 = -62.
n r = -2, g = (-^)(-32)-(^2)^64 + 2^^^^ * ' -2-1 -3 The solution is, r = 2, /S = — 62; or, r = — 2, /S = — 22.
The significanoe of the two answers is as follows : If r= 2, the progression 18—2, —4, —8, —16, —82, whose som is —02.
What to read after Advanced Course in Algebra?
You can find similar books in the "Read Also" column, or choose other free books by Webster Wells to read onlineMoreLess
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