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الكتب الكتب 1 - 10 من 17 فيIn every geometrical progression consisting of an odd number of terms ; the sum of....
" In every geometrical progression consisting of an odd number of terms ; the sum of the squares of the terms is equal to the sum of all the terms multiplied by the excess of the odd terms above the even. "
New series of The mathematical repository - الصفحة 53
بواسطة Thomas Leybourn - 1830
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Geometrical Problems Deducible from the First Six Books of Euclid, Arranged ...

Miles Bland - 1821 - عدد الصفحات: 438
...sum is equal to in times the sum of the same series with its terms inverted. 16. In every geometric progression consisting of an odd number of terms,...multiplied by the excess of the odd terms above the even. 17. If P be the product, S the sum, and « the sum of the reciprocals of n quantities in geometric...
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Examples in Arithmetic and Algebra: Collected and Arranged from TheCambridge ...

1834 - عدد الصفحات: 165
...the remaining terms; find the series. Answer, 1 + i + i + &c. 82. In every geometrical progression if an odd number of terms, the sum of the squares of...multiplied by the excess of the odd terms above the even. 83. In any geometrical progression if the (p + c)th term == m, and the (p — g)th = n, then will the...
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Mathematical problems and examples, arranged according to subjects, from the ...

1836
...being less than (a) that for the contrary. 41. Find the greatest term of the expansion of (a + 6)". 42. In every geometrical progression consisting of an...multiplied by the excess of the odd terms above the even. 43. Find the sum of 1 + | + | + \ + a, /3, j, .... being the coefficients of the expansion of (a -I-...
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Algebraical Problems: Producing Simple and Quadratic Equations, with Their ...

Miles Bland - 1841 - عدد الصفحات: 438
...sum is equal to m times the sum of the same series with its terms inverted. 16. In every geometric progression consisting of an odd number of terms,...multiplied by the excess of the odd terms above the even. 17. If P be the product, S the sum, and s the sum of the reciprocals of n quantities in geometric progression...
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A collection of problems and examples adapted to the 'Elementary course of ...

Harvey Goodwin (bp. of Carlisle.) - 1847 - عدد الصفحات: 80
...quantities in geometrical progression, and the sum of their reciprocals; find the quantities themselves. 11. In every geometrical progression consisting of an...multiplied by the excess of the odd terms above the even. 12. The difference of the means of 4 numbers in geometrical progression is 2, and the difference of...
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Examples in algebra

James Wharton - 1848 - عدد الصفحات: 151
...many terms of 6 + 4 + 2§+ &c. amount to 18. Ans. 3 + 6+12+ &c., 13J-4J+1J-&c. : and«. (458.) In any geometrical progression, consisting of an odd number...equal to the sum of all the terms multiplied by the difference of the odd and even terms. (459. ) In any geometrical progression, the sum of the first...
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The elements of algebra, المجلد 2

John William Colenso (bp. of Natal.) - 1849
...= a -„ — ¡~ ¿ nearly, a being the integer next 3/ "^* т ¿M greater than vN. 95. In every OP of an odd number of terms, the sum of the squares of the terms = product of sum of all the terms by excess of the odd terms above the even. 96. If the G. mean between...
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Miscellaneous Examples in Algebra: With Equation Papers Originally Proposed ...

John William Colenso - 1851 - عدد الصفحات: 94
...Shew that \/N = a - — — -s nearly, a being the integer next greater than -/Ж Уо. In every OP of an odd number of terms, the sum of the squares of the terms = product of sum of all the terms by excess of the odd terms above the even. 96. If the G. mean between...
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Exercises and problems in algebra [by J. Pryde] with answers

James Pryde - 1855
...176. 36. » i « « a « 1215, = 15, 45, 135, and 405. 37. » 5 » « 7 » 448, 38. In an equirational progression, consisting of an odd number of terms,...equal to the sum of all the terms multiplied by the difference of the odd and even terms ; required a proof. Let the progression be a + ar + ar2 + &c.,...
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Exercises and problems in algebra [by J. Pryde] with answers. without answers

James Pryde - 1855
...2304. 35. » 4 » » 11 » 352. 36. » 4 » » 5 » 1215. 37. « 5 aa 7 « 448. 38. In an equirational progression, consisting of an odd number of terms,...equal to the sum of all the terms multiplied by the difference of the odd and even terms ; required a proof. 39. If there be n equirational progressions,...
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