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第99頁

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$\frac{1}{4}$
$\frac{1}{8}$
$\frac{1}{16}$
310
31
496
?$=1-\frac {1}{2}+\frac {1}{2}-\frac {1}{3}+\frac {1}{3}-\frac {1}{4}+...+\frac {1}{99}-\frac {1}{100}$?
?$=1-\frac {1}{100}$?
?$= \frac {99}{100}$?
?$=(1+90)+(3+97)+(5+95)+...+(49+51)$?
?$=50×50$?
?$= 2500$?
已知?$\frac {3}{4×7}=\frac {1}{4}-\frac {1}{7}，$??$\frac {3}{7×10}=\frac {1}{7}-\frac {1}{10}。$?
?$ \frac {3}{4}+\frac {3}{28}+\frac {3}{70}+\frac {3}{130}+\frac {3}{208}$?
?$ =\frac {3}{4}+\frac {3}{4×7}+\frac {3}{7×10}+\frac {3}{10×13}+\frac {3}{13×16}$?
?$ =\frac {3}{4}+(\frac {1}{4}-\frac {1}{7})+(\frac {1}{7}-\frac {1}{10})+(\frac {1}{10}-\frac {1}{13})+(\frac {1}{13}-\frac {1}{16})$?
?$ =\frac {3}{4}+\frac {1}{4}-\frac {1}{7}+\frac {1}{7}-\frac {1}{10}+\frac {1}{10}-\frac {1}{13}+\frac {1}{13}-\frac {1}{16}$?
?$ =(\frac {3}{4}+\frac {1}{4})+(-\frac {1}{7}+\frac {1}{7})+(-\frac {1}{10}+\frac {1}{10})+(-\frac {1}{13}+\frac {1}{13})-\frac {1}{16}$?
?$ =1+0 + 0+0+0-\frac {1}{16}$?
?$ =1-\frac {1}{16}$?
?$ =\frac {15}{16}$?
?$C=(10 + 4)×2=14×2 = 28($?厘米?$)$?
?$ $?所以涂色部分兩個三角形的周長之和是?$28$?厘米。
100
99
98
97
和
?$100^2-99^2+98^2-97^2+... +2^2-1^2$?
?$ =(100 + 99)+(98 + 97)+...+(2 + 1)$?
?$ =(1 + 100)×100\div 2$?
?$ =101×100\div 2$?
?$ =5050$?
和
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