Question

Determine whether the infinite geometric series has a sum. If so, type the sum. If the sum is not an integer round to the nearest hundredth. If the sum diverges and the sum is undefined then just type none. 2+1.6+1.28+1.024+... What is the sum? Answer

Answer 1

Hi,

sum=10

Explanation:

`u_1=2\\u_2=1.6\\\\(u_3)/(u_2) =(1.28)/(1.6)= 0.8\\\\\\(u_(n+1))/(u_(n)) =0.8\\\\\\\displaystyle s=\sum_(i=1)^n\ (2*0.8^(i-1))=2*(0.8^n-1)/(0.8-1) \\\\ \lim_(i \to \infty) s= 2*(-1)/(0.2)=10\\`