Question

The population of a local species of dragon fly can be found using an infinite geometric series where a1=36 and the common ratio is 1/2 write the sum in sigma notation and calculate the sum that will be the upper limit of this population

Answer 1

Hello,


`a_0=72\\ a_1=72* (1)/(2)=36 \\ ...\\ a_i=72* (1)/(2^i) \\\\ \lim_(n \to \infty) \sum_(i=0)^(\infty)\ a_i = \lim_(n \to \infty)72* \sum_(i=0)^(\infty)\ (1)/(2^i) \\\\ =72* \lim_(n \to \infty) (1-(1)/(2^(n+1)))/(1-(1)/(2)) \\\\ =72*2=144`