Question

Identify the set as finite or infinite. {1,1/4 ,1/16 ,1/64 , . . .}

A. Finite
B. Infinite

Can someone explain this one for me?

Answer 1

Finite because the decimals end. If it was 1/3 then it would be infinite because the decimals would go on foreber

Answer 2

`1;\ (1)/(4);\ (1)/(16);\ (1)/(64);...\\\\a_1=(1)/(4^(1-1))=(1)/(4^0)=(1)/(1)=1\\\\a_2=(1)/(4^(2-1))=(1)/(4^1)=(1)/(4)\\\\a_3=(1)/(4^(3-1))=(1)/(4^2)=(1)/(16)\\\\a_4=(1)/(4^(4-1))=(1)/(4^3)=(1)/(64)\\\vdots\\a_n=(1)/(4^(n-1))`


`\lim\limits_(n\to\infty)(1)/(4^(n-1))=\lim\limits_(n\to\infty)(1)/(4^n\cdot4^(-1))=\lim\limits_(n\to\infty)(1)/(4^n\cdot(1)/(4))=\lim\limits_(n\to\infty)(4)/(4^n)=0\\\\\\Answer:A`