｛an}等比数列,且an>0,a1*a100=100 则 lga1+lga2+...+lga100=

lga1+lga2+...+lga100=lga1*a2*.*a99*a100由｛an}等比数列,得a1*a100=a2*a99=a3*a98=.=a50*a51=100而a1*a2*.*a99*a100=a1*a100*a2*a99*a3*a98*.*a50*a51=100^(100/2)=100^50=10^100从而 lga1+lga2+...+lga100=lga1*a...