1784•Philosophical Transactions of the Royal Society of LondonRequires access

XXVIII. On the summation of series, whose general term is a determinate function of z the distance from the first term of the series

Edward Waring

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Abstract

PROBLEM. The sum S being given, to find a series of which it is the sum. 1. Reduce the sum S into a converging series, proceeding according to the dimensions of any small quantities, and it is done, For example: let any algebraical function S of an unknown or small quantity x be assumed, reduce it into a converging series proceeding according to the dimension of x, and there results a series whose sum is S.

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PROBLEM. The sum S being given, to find a series of which it is the sum. 1. Reduce the sum S into a converging series, proceeding according to the dimensions of any small quantities, and it is done, For example: let any algebraical function S of an unknown or small quantity x be assumed, reduce it into a converging series proceeding according to the dimension of x, and there results a series whose sum is S.

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Available abstract

PROBLEM. The sum S being given, to find a series of which it is the sum. 1. Reduce the sum S into a converging series, proceeding according to the dimensions of any small quantities, and it is done, For example: let any algebraical function S of an unknown or small quantity x be assumed, reduce it into a converging series proceeding according to the dimension of x, and there results a series whose sum is S.

Key concepts: Series (stratigraphy), Term (time), Alternating series, Mathematics, Dimension (graph theory), Function series, Function (biology), Geometric series

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XXVIII. On the summation of series, whose general term is a determinate function of z the distance from the first term of the series — Research Paper | ScholarLens