A Simple Method of Enlarging the Convergence Region of Newtonian Binomial Expression (1+t)￣αto Infinity

In this paper,using a simple algebraic transformation, the author proposes a generalized binomial expression about the real function(1+t)α(α≠0,1,2,… ),and proves that it converges to(1+t)α in the region for all real values of α(α≠0, 1,2,…) and even in the region for all such values of a that(1+t)α has meanings at t-1. Thus,as k tends to zero,the convergence region tends to infinity so that the general Newtonian binomial expression can converge to (1+t)αin the whole region where (1+t)α has meanings.Moreover,the classical Newtonian binomial expression is a special case of it at