在等比数列中an若an>0 a1a100=100 则 lga1+lga2+lga3+……+lga100
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在等比数列中an若an>0 a1a100=100 则 lga1+lga2+lga3+……+lga100
lga1+lga2+lga3+……+lga100
=lg(a1a2a3a……a100)
=lg[(a1a100)(a2a99)(a3a98)……(a50a51)]
因为a1a100=a2a99=a3a98=……=a50a51 共50组所以
lga1+lga2+lga3+……+lga100
=lg(a1a2a3a……a100)
=lg[(a1a100)(a2a99)(a3a98)……(a50a51)]
=lg(a1a100)^50
=50lg(a1a100)
=50lg100
=100
很高兴为您解答,希望对你有所帮助!
>>>>>>>>>>>>>>>>【神机易数】团队
=lg(a1a2a3a……a100)
=lg[(a1a100)(a2a99)(a3a98)……(a50a51)]
因为a1a100=a2a99=a3a98=……=a50a51 共50组所以
lga1+lga2+lga3+……+lga100
=lg(a1a2a3a……a100)
=lg[(a1a100)(a2a99)(a3a98)……(a50a51)]
=lg(a1a100)^50
=50lg(a1a100)
=50lg100
=100
很高兴为您解答,希望对你有所帮助!
>>>>>>>>>>>>>>>>【神机易数】团队
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