等比数列 an>0 a1xa100=100 lga1+lga2+lga3+……lga100=?

来源:学生作业帮助网 编辑:六六作业网 时间:2024/11/27 01:59:29
等比数列an>0a1xa100=100lga1+lga2+lga3+……lga100=?等比数列an>0a1xa100=100lga1+lga2+lga3+……lga100=?等比数列an>0a1xa

等比数列 an>0 a1xa100=100 lga1+lga2+lga3+……lga100=?
等比数列 an>0 a1xa100=100 lga1+lga2+lga3+……lga100=?

等比数列 an>0 a1xa100=100 lga1+lga2+lga3+……lga100=?
因为等比数列 an>0 a1*a100=100
所以a1*a100=a2*a99=……a49*a52=a50*a51=100
也即共计100/2=50个100
那么lga1+lga2+lga3+……lga100=lg(a1*a100)+lg(a2*a99)……=50*2=100

a1*a100=a2*a99=a3*a98=.....=a50*a51=100,原式=lga1*a2*...*a100=lg(100)^50=100