Toán Lớp 6: Tính tích sau :
( 1 – 1/2 ) ( 1 – 1/3 ) ( 1- 1/4 ) … ( 1 – 1/49 ) ( 1 – 1/50 )
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Toán Lớp 6: Tính tích sau :
( 1 – 1/2 ) ( 1 – 1/3 ) ( 1- 1/4 ) … ( 1 – 1/49 ) ( 1 – 1/50 )
Comments ( 2 )
(1-1/2)(1-1/3)(1-1/4)…..(1-1/49)(1-1/50)
=1/2 . 2/3 .3/4 ….. 48/49 .49/50
=\frac{1.2.3.4….48.49}{2.3.4…49.50}
=1/50
Answer
(1 – 1/2) . (1 – 1/3) . (1 – 1/4) … (1 – 1/49) . (1 – 1/50)
= (2/2 – 1/2) . (3/3 – 1/3) . (4/4 – 1/4) … (49/49 – 1/49) . (50/50 – 1/50)
= 1/2 . 2/3 . 3/4 … 48/49 . 49/50
= {1 . 2 . 3 …. 48 . 49}/{2 . 3 . 4 … 49 . 50}
= 1/50