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Ta thấy:
1/7 + 1/14 + 1/28 = (4+2+1)/28 = 1/4
1/8 + 1/12 + 1/24 = (3+2+1)/24 = 1/4
1/11 + 1/22 + 1/33 = (6+3+2)/66 = 1/6
1/9 + 1/18 = (2+1)/18 = 1/6
Mà 1/4 + 1/4 = 1/2 và 1/6 + 1/6 = 1/3
Nên:
1/10 + 1/13 + 1/15 + 1/2 + 1/3 =
1/10 + 1/13 + 1/15 + 5/10 + 5/15 =
6/10 + 6/15 + 1/13 =
3/5 + 2/5 + 1/13 =
1 + 1/13 = 14/13
TT ik nha bạn ))))
a)Tính bằng cách thuận tiện nhất:
1/7+1/8+1/9+1/10+1/11+1/12+1/13+1/14+1/15+1/18+1/22+1/24+1/28+1/33
Giải
Ta thấy:
1/7 + 1/14 + 1/28 = (4+2+1)/28 = 1/4
1/8 + 1/12 + 1/24 = (3+2+1)/24 = 1/4
1/11 + 1/22 + 1/33 = (6+3+2)/66 = 1/6
1/9 + 1/18 = (2+1)/18 = 1/6
Mà 1/4 + 1/4 = 1/2 và 1/6 + 1/6 = 1/3
Nên:
1/10 + 1/13 + 1/15 + 1/2 + 1/3 =
1/10 + 1/13 + 1/15 + 5/10 + 5/15 =
6/10 + 6/15 + 1/13 =
3/5 + 2/5 + 1/13 =
1 + 1/13 = 14/13
a/ 1+4+7+10+....+52+55+58-410=[(58-1):3+1]x(58+1)-410=20x59-410=770
mình chưa tính nhung mà cách tính:
rút gọn rồi gạch những số giống nhau và tính tổng số đó
nhác tính
\(\frac{1}{7}+\frac{1}{14}+\frac{1}{28}=\frac{1}{4}\)
\(\frac{1}{8}+\frac{1}{12}+\frac{1}{24}=\frac{1}{4}\)
\(\frac{1}{11}+\frac{1}{22}+\frac{1}{33}=\frac{1}{6}\)
\(\frac{1}{9}+\frac{1}{18}=\frac{1}{6}\)
\(\frac{1}{10}+\frac{1}{15}=\frac{1}{6}\)
=>BT=\(\frac{1}{4}.2+\frac{1}{6}.3=1\)
\(a,=\frac{7-1}{1.3.7}+\frac{9-3}{3.7.9}+\frac{13-7}{7.9.13}+\frac{15-9}{9.13.15}\)\(+\frac{19-13}{13.15.19}\)
\(=\frac{1}{1.3}-\frac{1}{3.7}+\frac{1}{3.7}-\frac{1}{7.9}+\frac{1}{7.9}-\frac{1}{9.13}+\frac{1}{9.13}-\frac{1}{13.15}+\frac{1}{13.15}-\frac{1}{15.19}\)
\(=\frac{1}{1.3}-\frac{1}{15.19}=\frac{95}{285}-\frac{1}{285}=\frac{94}{285}\)
\(b,=\frac{1}{6}.\left(\frac{6}{1.3.7}+\frac{6}{3.7.9}+\frac{6}{7.9.13}+\frac{6}{9.13.15}+\frac{6}{13.15.19}\right)\)
làm giống như trên
\(c,=\frac{1}{8}.\left(\frac{1}{1.2.3}+\frac{1}{2.3.4}+\frac{1}{3.4.5}+...+\frac{1}{48.49.50}\right)\)
\(=\frac{1}{16}.\left(\frac{2}{1.2.3}+\frac{2}{2.3.4}+\frac{2}{3.4.5}+...+\frac{2}{48.49.50}\right)\)
\(=\frac{1}{16}.\left(\frac{3-1}{1.2.3}+\frac{4-2}{2.3.4}+\frac{5-3}{3.4.5}+...+\frac{50-48}{48.49.50}\right)\)
\(=\frac{1}{16}.\left(\frac{1}{1.2}-\frac{1}{2.3}+\frac{1}{2.3}-\frac{1}{3.4}+\frac{1}{3.4}-\frac{1}{4.5}+...+\frac{1}{48.49}-\frac{1}{49.50}\right)\)
\(=\frac{1}{16}.\left(\frac{1}{2}-\frac{1}{2450}\right)=\frac{1}{16}.\left(\frac{1225}{2450}-\frac{1}{2450}\right)=\frac{153}{4900}\)
\(d,=\frac{5}{7}.\left(\frac{7}{1.5.8}+\frac{7}{5.8.12}+\frac{7}{8.12.15}+...+\frac{7}{33.36.40}\right)\)
\(=\frac{5}{7}.\left(\frac{8-1}{1.5.8}+\frac{12-5}{5.8.12}+\frac{15-8}{8.12.15}+...+\frac{40-33}{33.36.40}\right)\)
\(=\frac{5}{7}.\left(\frac{1}{1.5}-\frac{1}{5.8}+\frac{1}{5.8}-\frac{1}{8.12}+\frac{1}{8.12}-\frac{1}{12.15}+...+\frac{1}{33.36}-\frac{1}{36.40}\right)\)
\(=\frac{5}{7}.\left(\frac{1}{5}-\frac{1}{1440}\right)=\frac{5}{7}.\left(\frac{288}{1440}-\frac{1}{1440}\right)=\frac{41}{288}\)
P/S: . là nhân nha
=(1/7+1/14+1/28)+(1/8+1/12+1/24)+(1/11+1/22+1/33)+(1/9+1/18)+(1/10+1/15)
=1/4+1/4+1/6+1/6+1/6
=1/4*2+1/6*3=1