Summation - Growth Rates

Growth Rates

The following are useful approximations (using theta notation):

for real c greater than −1
(See Harmonic number)
for real c greater than 1
for non-negative real c
for non-negative real c, d
for non-negative real b > 1, c, d

Read more about this topic:  Summation

Famous quotes containing the words growth and/or rates:

    Hence, the less government we have, the better,—the fewer laws, and the less confided power. The antidote to this abuse of formal Government, is, the influence of private character, the growth of the Individual; the appearance of the principal to supersede the proxy; the appearance of the wise man, of whom the existing government, is, it must be owned, but a shabby imitation.
    Ralph Waldo Emerson (1803–1882)

    Families suffered badly under industrialization, but they survived, and the lives of men, women, and children improved. Children, once marginal and exploited figures, have moved to a position of greater protection and respect,... The historic decline in the overall death rates for children is an astonishing social fact, notwithstanding the disgraceful infant mortality figures for the poor and minorities. Like the decline in death from childbirth for women, this is a stunning achievement.
    Joseph Featherstone (20th century)