Question

!30 баллов! (7 класс) -Не фото-
Найдите последовательно значение каждой из разностей:
$frac{1}{2}- frac{1}{3}, frac{1}{3}-frac{1}{4},frac{1}{4}-frac{1}{5},frac{1}{5}-frac{1}{6},frac{1}{6}-frac{1}{7},frac{1}{7}-frac{1}{8}$
а затем значение суммы $frac{1}{6}+ frac{1}{12}+ frac{1}{20}+ frac{1}{30}+ frac{1}{42}+ frac{1}{56}$

Answer 1

1/2-1/3=3/6-2/6=1/6
1/3-1/4=4/12-3/12=1/12
1/4-1/5=5/20-4/20=1/20
1/5-1/6=6/30-5/30=1/30
1/6-1/7=7/42-6/42=1/42
1/7-1/8=8/56-7/56=1/56

1/6+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