Question 39
Given the series $2+1+\dfrac12+\dfrac14+\cdots$ and the following five statements:
$(1)$ the sum increases without limit.
$(2)$ the sum decreases without limit.
$(3)$ the difference between any term of the sequence and zero can be made less than any positive quantity no matter how small.
$(4)$ the difference between the sum and $4$ can be made less than any positive quantity no matter how small.
$(5)$ the sum approaches a limit.
Of these statements, the correct ones are:
$(1)$ the sum increases without limit.
$(2)$ the sum decreases without limit.
$(3)$ the difference between any term of the sequence and zero can be made less than any positive quantity no matter how small.
$(4)$ the difference between the sum and $4$ can be made less than any positive quantity no matter how small.
$(5)$ the sum approaches a limit.
Of these statements, the correct ones are: