计算,1/(1*4)+1/(4*7)+1/(7*10)+1/(10*13)......1/(97*100)
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1/(1*4)+1/(4*7)+1/(7*10)+1/(10*13)......1/(97*100)
=(1/3)*(1-1/4)+(1/3)*(1/4-1/7)+(1/3)*(1/7-1/10)+(1/3)*(1/10-1/13)。。。
(1/3)*(1/94-1/97)+ (1/3)*(1/97-1/100)
=(1/3)*(1-1/4+1/4-1/7+1/7-1/10+1/10-1/13.。。。+1/94-1/97+1/97-1/100)
=(1/3)*(1-1/100)
=(1/3)*(99/100)
=33/100
=0.33
=(1/3)*(1-1/4)+(1/3)*(1/4-1/7)+(1/3)*(1/7-1/10)+(1/3)*(1/10-1/13)。。。
(1/3)*(1/94-1/97)+ (1/3)*(1/97-1/100)
=(1/3)*(1-1/4+1/4-1/7+1/7-1/10+1/10-1/13.。。。+1/94-1/97+1/97-1/100)
=(1/3)*(1-1/100)
=(1/3)*(99/100)
=33/100
=0.33
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