Toán Lớp 6: 3/1.5+3/5.9+3/9.19+…+3/45.49
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Toán Lớp 6: 3/1.5+3/5.9+3/9.19+…+3/45.49
Comments ( 2 )
Giải đáp:
36/49
Lời giải và giải thích chi tiết:
C1: 3/(1*5)+3/(5*9)+3/(9*13)+…+3/(45*49)
= 3/4 * 4/(1*5) + 3/4*4/(5*9)+3/4*4/(9*13)+…+3/4*4/(45/49)
= 3/4 *(4/(1*5) + 4/(5*9)+4/(9*13)+…+4/(45*49))
= 3/4*(1/1-1/5+1/5-1/9+1/9-1/13+….+1/45-1/49)
= 3/4*(1/1-1/49)
= 3/4*48/49
= 36/49
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C2: 3/(3*5)+3/(5*9)+3/(9*13)+…+3/(45*49)
= (1/1 – 1/5 – 1/(1*5))+(1/5-1/9-1/(5*9))+(1/9-1/13-1/(9*13))+…+(1/45-1/49-1/(45*49))
= 1/1 – 1/5 – 1/(1*5) + 1/5 – 1/9-1/(5*9)+1/9-1/13-1/(9*13)+…+1/45-1/49-1/(45*49)
= 1/1 – 1/5 – (1/1-1/5):4+1/5-1/9-(1/5-1/9):4+1/9-1/13-(1/9-1/13):4+…+1/45-1/49-(1/45-1/49):4
= 1/1 – 1/5 – (1/4-1/20)+1/5-1/9-(1/20-1/36)+1/9-1/13-(1/36-1/52)+…+1/45-1/49-(1/180-1/196)
= 1/1 – 1/5 – 1/4 + 1/20 + 1/5-1/9-1/20+1/36+1/9-1/13-1/36+1/52+…+1/45-1/49-1/180+1/196
=(1/1-1/5+1/5-1/9+1/9-1/13+…+1/45-1/49) + (1/4+1/20-1/20+1/36-…-1/180+1/196)
= (1/1-1/49) + (-1/4 – 1/196)
= 48/49 + (-12)/49
= 36/49
*** Đề được sửa chữa ở phần hỏi chi tiết ***
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3/( 1 . 5 ) + 3/( 5 . 9 ) + 3/( 9 . 13 ) + …. + 3/( 45 . 49 )
= 3/4 . ( 4/( 1 . 5 ) + 4/( 5 . 9 ) + 4/( 9 . 13 ) + …. + 4/( 45 . 49 ) )
= 3/4 . ( 1/1 – 1/5 + 1/5 – 1/9 + 1/9 – 1/13 + …. + 1/45 – 1/49 )
= 3/4 . ( 1 – 1/49 )
= 3/4 . 48/49
= 36/49