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Найдите последовательно значение каждой из разностей:
[tex] \frac{1}{2}- \frac{1}{3}, \frac{1}{3}-\frac{1}{4},\frac{1}{4}-\frac{1}{5},\frac{1}{5}-\frac{1}{6},\frac{1}{6}-\frac{1}{7},\frac{1}{7}-\frac{1}{8}[/tex]
а затем значение суммы [tex] \frac{1}{6}+ \frac{1}{12}+ \frac{1}{20}+ \frac{1}{30}+ \frac{1}{42}+ \frac{1}{56}[/tex]

1/2-1/3=3/6-2/6=1/61/3-1/4=4/12-3/12=1/121/4-1/5=5/20-4/20=1/201/5-1/6=6/30-5/30=1/301/6-1/7=7/42-6/42=1/421/7-1/8=8/56-7/56=1/561/6+1/12+1/20+1/30+1/42+1/56=(1/6+1/12)+(1/20+1/30)+1/42+1/56= =(2/12+1/12)+ (3/60+2/60)+1/42+1/56=  =3/12+5/60+1/42+1/56= 3/12+1/12+1/42+1/56= =4/12+1/42+1/56=1/3+1/42+1/56=14/42+1/42+1/56=15/42+1/56=5/14+1/56= =20/56+1/56=21/56