Name the mathematician who gave general expression for the sum of infinite geometric series.?

Question

related to france

Answer 1

The idea of an infinite series expansion of a function was first conceived in India by Madhava in the 14th century, who also developed the concepts of the power series, the Taylor series, the Maclaurin series, rational approximations of infinite series, and infinite continued fractions. He discovered a number of infinite series, including the Taylor series of the trigonometric functions of sine, cosine, tangent and arctangent, the Taylor series approximations of the sine and cosine functions, and the power series of the radius, diameter, circumference, angle θ, π and π/4. His students and followers in the Kerala School further expanded his works with various other series expansions and approximations, until the 16th century.

In the 17th century, James Gregory also worked on infinite series and published several Maclaurin series. In 1715, a general method for constructing the Taylor series for all functions for which they exist was provided by Brook Taylor. Leonhard Euler in the 18th century, developed the theory of hypergeometric series and q-series.

In Europe however, the investigation of the validity of infinite series is considered to begin with Gauss in the 19th century. Euler had already considered the hypergeometric series on which Gauss published a memoir in 1812.

Answer 2

The sum of the components of an arithmetic progression is called an arithmetic series. The formula for the sum of the first n terms of an arithmetic progression is:


This formula is derived from the fact that the sum of the first and the last term is the same as the sum of the second and the second last, and so forth. An often-told story is that Carl Friedrich Gauss discovered it when his third grade teacher asked the class to find the sum of the first 100 numbers, and he instantly computed the answer (5050).

Answer 3

I'm not sure but my guess would be Euler, e is named after Euler and e is an infinite geometric series.

Answer 4

The formulation for the sum of an endless geometric sequence is A1 / (a million-r) as long as |r|

Answer 5

Xeno

Answer 6

The father ''Sébastien Truchet'' found the geometrical progression: 7,5,9,10,5,12,15,18,21,24,...

Answer 7

Rene Descartes?
Or perhaps it was Lagrange