Answer:1) not diverges2)not diverges3) diverges4)not divergesStep-by-step explanation:In geometric series, If the |r|<1 then the series is convergent and if |r|>1 then the series is divergentWhere r is the ratio between the consecutive terms of series.1) 3/5 + 3/10 +3/20 + 3/40 ......in the above geometric series r= (3/10) / (3/5) = 1/2 = 0.5As |r|= 0.5 < 1, so the series will not diverge2) -10+4-8/5 + 16/25 -......in the above geometric series r= (4) / (-10) = -2/5 = -0.4As |r|= 0.4 < 1, so the series will not diverge3) ∑ 2/3(-4)^(n-1)in the above geometric series r= -4As |r|= |-4| = 4 > 1, so the series will diverge4) ∑ (-12)(1/5)^(n-1)in the above geometric series r=1/5 = 0.2As |r|= 0.2 < 1, so the series will not diverge !