Question

几道小学六年级奥数题(简便运算)

1/1*3+1/3*5+1/5*7+……+1/47*49
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1/2*5+1/3*5+1/8*11+……+1/20*23
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3/4+7/12-9/20+11/30-13/42
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2002/1*3+2002/3*5+2002/5*7+2002/7*9+2002/9*11
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最好写上过程,解题思路.

Answer 1

1/1*3+1/3*5+1/5*7+……+1/47*49
= 1/2(1-1/3)+........1/2(1/47-1/49)
= 1/2(1-1/3+1/3-1/5+.......+1/47-1/49)
=24/49
1/2*5+1/3*5+1/8*11+……+1/20*23
=
=
3/4+7/12-9/20+11/30-13/42
=(1-1/4+1/4+1/3-1/4-1/5+1/5+1/6-1/6-1/7)
= 1+1/3-1/4-1/7
=79/84
2002/1*3+2002/3*5+2002/5*7+2002/7*9+2002/9*11
=2002(1/1*3+1/3*5+...+1/9*11)
=2002[1/2(1-1/3)+1/2(1/3-1/5)+...+1/2(1/9-1/11)
=2002*5/11
=910