Module 1 Tasks Hints | References Table of Modules

Computation of mathematical constants and of values of elementary functions as limits of infinite convergent sequences Algorithms for acceleration of convergence of infinite convergent sequences

1.1.

Investigate the convergence behaviour of the infinite convergent sequences defined by

;	(1)
;	(2)
;	(3)
;	(4)
;	(5)

1.2.

By the use of experiments, try to find algorithms which accelerate the convergence of these sequences, i.e. develop transformations of each sequence <> into another sequence with

	(6)
	(7)

so each yields significantly more valid decimal digits of than for .