Question

For a TRUE statement you must explain and prove in general why it is true. For a FALSE statement you must give a COUNTEREXAMPLE. For example of a counterexample, if the state- ment was "An even number divided by an even number is always ever" your counterexample could be 6 : 2 = 3 where 6 and 2 are even but 3 is obviously odd.

Answer the four of them, please

Answer 1

Then 7 Suppose z an conververges z fan converges. Amy- It is fulse. Because An = then n² Ean En is a p-series with 6 = 21 So it is convergent And Jonath then n p-series with p = 1 E ran=F is a so it is divergent Hence, the giren statement is false 8 Suppose Ean diverges. Then Sequence also diverges Ans: is fulse. Un=Yn then Z u is diverges shown But Yn ie convergent. that It Let asi cabove sequence is an =

Because lim ana lim no nyo n Hence, the given statement in fulse 9 Z 1 2 3 4 ++372 no Because series, I Ami- The giren statement is teve the given series Z is geometric with 6) ( perut term of series) & ratio -2 / 151 = 3/<1 So it's convergent And (-3/)" ar r = . I 1- (-3/2) I 1 + 3/2

Hence, the given statement is True lop It Ean converges then Eé an همه رومیزی Amit The given statement is True Because Suppose E an is convergent. So, fror com the Zero test, lim cn = nya otherwise it is divergent Mor, for Jean lim an lim an nos = e nyo = e 130

Zoro test, the series an e ês So from the Z diverges. Hence, the given statement to Hope Hope this is helpful! is teve ve is