1.计算:(1+2/3)*(1+2/5)*(1+2/7)**(1
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亲，您好！
很高兴为您回答这个问题。
1. 计算:
(1+2/3) × (1+2/5) × (1+2/7) × ... × (1+2/99) × (1-2/3) × (1-2/5) × ... × (1-2/99)
= (1+2/3) × (1+2/5) × ... × (1+2/99) × (1-2/3) × (1-2/5) × ... × (1-2/99)
= 5/3 × 7/5 × ... × 101/97 × 1/3 × 3/5 × ... × 97/99
= 1/3 × 101 × 1/99
= 101/297
咨询记录 · 回答于2024-01-04
1.计算:(1+2/3)*(1+2/5)*(1+2/7)**(1
亲，链宴您好很高兴为您回答滚穗这个问题哦~，棚备银
1. 计算:
(1+2/3) × (1+2/5) × (1+2/7) × ... × (1+2/99) × (1-2/3) × (1-2/5) × ... × (1-2/99)
= (1+2/3) × (1+2/5) × ... × (1+2/99) × (1-2/3) × (1-2/5) × ... × (1-2/99)
= 5/3 × 7/5 × ... × 101/97 × 1/3 × 3/5 × ... × 97/99
= 1/3 × 101 × 1/99
= 101/297
，棚备银
1. 计算:
(1+2/3) × (1+2/5) × (1+2/7) × ... × (1+2/99) × (1-2/3) × (1-2/5) × ... × (1-2/99)
= (1+2/3) × (1+2/5) × ... × (1+2/99) × (1-2/3) × (1-2/5) × ... × (1-2/99)
= 5/3 × 7/5 × ... × 101/97 × 1/3 × 3/5 × ... × 97/99
= 1/3 × 101 × 1/99
= 101/297
这题怎么解？
=(5/3)*(1/3)*(7/5)*(3/5)*...*(101/99)*(97/99)=(1/3)*(5/3)*(3/5)*(7/5)*...*(97/99)*(101/99)=1/3*101/99=101/297
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