Tính nhanh hợp lí:
a)\(A=\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+...+\frac{1}{600}\)
b)\(B=\frac{-5}{3}+\frac{-5}{15}+\frac{-5}{35}+...+\frac{-5}{2499}\)
Tính nhanh hợp lí:
\(B=\frac{-5}{3}+\frac{-5}{15}+\frac{-5}{35}+....+\frac{-5}{2499}\)
Ta có:
B = \(\frac{-5}{3}+\frac{-5}{15}+\frac{-5}{35}+...+\frac{-5}{2499}.\)
= \(-5\left(\frac{1}{3}+\frac{1}{15}+\frac{1}{35}+...+\frac{1}{2499}\right)\)
= \(-5\left(\frac{1}{1.3}+\frac{1}{3.5}+\frac{1}{5.7}+...+\frac{1}{49.51}\right)\)
= \(-5\left(1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+...+\frac{1}{49}-\frac{1}{51}\right):2\)
= \(\frac{-5}{2}\left(1-\frac{1}{51}\right)\)
= \(\frac{-5}{2}.\frac{50}{51}\) = -6375
Tính nhanh hợp lí:
\(B=\frac{-5}{3}+\frac{-5}{15}+\frac{-5}{35}+...+\frac{-5}{2499}\)
\(B=\frac{-5}{3}+\frac{-5}{15}+\frac{-5}{35}+...+\frac{-5}{2499}\)
\(B=\frac{-5}{1.3}+\frac{-5}{3.5}+\frac{-5}{5.7}+...+\frac{-5}{49.51}\)
\(B=\frac{-5}{2}\left(\frac{2}{1.3}+\frac{2}{3.5}+\frac{2}{5.7}+...+\frac{2}{49.51}\right)\)
\(B=\frac{-5}{2}.\left[\left(1-\frac{1}{3}\right)+\left(\frac{1}{3}-\frac{1}{5}\right)+...+\left(\frac{1}{49}-\frac{1}{51}\right)\right]\)
\(B=\frac{-5}{2}.\left[1-\left(\frac{1}{3}-\frac{1}{3}\right)+\left(\frac{1}{5}-\frac{1}{5}\right)+...+\left(\frac{1}{49}-\frac{1}{49}\right)-\frac{1}{51}\right]\)
\(B=\frac{-5}{2}.\left(1-\frac{1}{51}\right)=\frac{-5}{2}.\frac{50}{51}=\frac{-125}{51}\)
=-5/1.3+-5/3.5+-5/5.7+.............+-5/49.51
-5/2(1-1/51)
=-125/51
ai k mk mk k lai
ok
B = -5/1.3 + -5/3.5 +.....+ -5/49.51
B = -5/2(1 - 1/51)
B = -5/2 . 50/51
B = -125/51 nha!
Tính bằng cách hợp lí:
a) \(\frac{15}{12}+\frac{5}{13}-\frac{3}{12}-\frac{18}{13}\) ( Phép này tính bằng 1 nhưng lại sai mất)
b) \(\frac{13}{25}+\frac{6}{41}-\frac{38}{25}+\frac{35}{41}-\frac{1}{2}\)
c) \(\left(\frac{1}{2}-\frac{2}{3}\right)-\left(\frac{5}{3}-\frac{3}{2}\right)+\left(\frac{7}{3}-\frac{5}{2}\right)\)
Help me!!!!! Nhanh nhé, 15' thui
\(a,=\left(\frac{15}{12}-\frac{3}{12}\right)+\left(\frac{5}{13}-\frac{18}{13}\right)\)
\(=1+-1\)
\(=0\)
Tính:
a) \(\frac{5}{1.4}+\frac{5}{4.7}+...+\frac{5}{100.103}\)
b) \(\frac{1}{15}+\frac{1}{35}+...+\frac{1}{2499}\)
a)\(\frac{5}{1.4}+\frac{5}{4.7}+...+\frac{5}{100.103}=\frac{5}{3}\cdot\left(\frac{3}{1.4}+\frac{4}{4.7}+...+\frac{3}{100.103}\right)\)
\(=\frac{5}{3}\cdot\left(1-\frac{1}{4}+\frac{1}{4}-\frac{1}{7}+...+\frac{1}{100}-\frac{1}{103}\right)=\frac{5}{3}\cdot\left(1-\frac{1}{103}\right)=\frac{5}{3}\cdot\frac{102}{103}=\frac{170}{103}\)b)\(\frac{1}{15}+\frac{1}{35}+...+\frac{1}{2499}=\frac{1}{3.5}+\frac{1}{5.7}+...+\frac{1}{49.51}\)
\(\frac{1}{2}\cdot\left(\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+...+\frac{1}{49}-\frac{1}{51}\right)=\frac{1}{2}\cdot\left(\frac{1}{3}-\frac{1}{51}\right)=\frac{1}{2}\cdot\frac{16}{51}=\frac{8}{51}\)
Câu a) bạn Ác Mộng làm rồi nên mình làm b) nha
b)Gọi A = \(\frac{1}{15}+\frac{1}{35}+...+\frac{1}{2499}\)
\(A=\frac{1}{3.5}+\frac{1}{5.7}+...+\frac{1}{49.51}\)
\(2A=2.\left(\frac{1}{3.5}+\frac{1}{5.7}+...+\frac{1}{49.51}\right)\)
\(2A=\frac{2}{3.5}+\frac{2}{5.7}+...+\frac{2}{49.51}\)
\(2A=\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+...+\frac{1}{49}-\frac{1}{51}\)
\(2A=\frac{1}{3}-\frac{1}{51}\)
\(2A=\frac{16}{51}\)
\(A=\frac{16}{51}:2\)
\(A=\frac{8}{51}\)
5*(5-5/4+5/4-5/7+.......+5/100-5/103)
5*(5-5/103)
5*......... bạn tự tính nhé
câu b 1/3*5+1/5*7+............+1/49*51
1*(1/1-1/3+1/3-1/5+............+1/49-1/51)
1/1-1/51 tính ra rồi ra kết quả
tk nha
1) a/ Tính:
\(1-\frac{1}{2};\frac{1}{2}-\frac{1}{3};\frac{1}{3}-\frac{1}{4};\frac{1}{4}-\frac{1}{5};\frac{1}{5}-\frac{1}{6}\)
Sử dụng kết quả của câu a/ để tính nhanh tổng sau :
\(\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+\frac{1}{30}\)
2)a/Tính nhanh:
B= \(\frac{1}{15}+\frac{1}{35}+\frac{1}{63}+\frac{1}{99}+\frac{1}{143}\)
b/ Tính nhanh:
C= \(\frac{1}{2}+\frac{1}{14}+\frac{1}{35}+\frac{1}{65}+\frac{1}{104}+\frac{1}{152}\)
Bài 1 : tính theo cách hợp lý nhất
\(\frac{6}{11}+\frac{1}{3}+\frac{5}{11}\)
Bài 2 : Tính bằng cách nhanh nhất
\(\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+\frac{1}{20}\)
Bài 3 : Tính nhanh
a,\(\frac{3}{2}\times\frac{4}{5}\times\frac{2}{3}\)
b,\(\frac{6}{7}\times\subset\frac{5}{3}\times\frac{7}{6}\supset\)
Bài 4 : Tính nhanh
a,\(\frac{2}{5}\times\frac{1}{4}+\frac{3}{4}\times\frac{2}{5}\)
b,\(\frac{6}{11}\div\frac{2}{3}+\frac{5}{11}\div\frac{2}{3}\)
bài 1:
\(\frac{6}{11}+\frac{1}{3}+\frac{5}{11}\)
\(=\left(\frac{6}{11}+\frac{5}{11}\right)+\frac{1}{3}\)
\(=\frac{11}{11}+\frac{1}{3}=1+\frac{1}{3}=\frac{3}{3}+\frac{1}{3}=\frac{4}{3}\)
bài 2:
\(\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+\frac{1}{20}\)
\(=\left(\frac{1}{2}+\frac{1}{20}\right)+\left(\frac{1}{6}+\frac{1}{12}\right)\)
\(=\frac{11}{20}+\frac{1}{4}=\frac{11}{20}+\frac{5}{20}=\frac{15}{20}=\frac{3}{4}\)
bài 3:
a) \(\frac{3}{2}\cdot\frac{4}{5}\cdot\frac{2}{3}=\left(\frac{3}{2}\cdot\frac{2}{3}\right)\cdot\frac{4}{5}=1\cdot\frac{4}{5}=\frac{4}{5}\)
b) \(\frac{6}{7}\cdot\frac{5}{3}\cdot\frac{7}{6}=\left(\frac{6}{7}\cdot\frac{7}{6}\right)\cdot\frac{5}{3}=1\cdot\frac{5}{3}=\frac{5}{3}\)
bài 4:
a) \(\frac{2}{5}\cdot\frac{1}{4}+\frac{3}{4}\cdot\frac{2}{5}=\frac{2}{5}\cdot\left(\frac{1}{4}+\frac{3}{4}\right)=\frac{2}{5}\cdot1=\frac{2}{5}\)
b) \(\frac{6}{11}:\frac{2}{3}+\frac{5}{11}:\frac{2}{3}=\left(\frac{6}{11}+\frac{5}{11}\right):\frac{2}{3}=1:\frac{2}{3}=\frac{3}{2}\)
Bài 1:
6/11 + 1/3 + 5/11
= ( 6/11 + 5/11) + 1/3
= 11/11 + 1/3
= 1 + 1/3
= 3/3 +1/3
= 4/3
Bài 2:
1/2 + 1/6 + 1/12 + 1/20
= ( 1/2 + 1/6 + 1/12 ) + 1/20
= ( 6/12 + 2/12 + 1/12 ) + 1/20
=9/12 + 1/20
= 3/4 +1/20
= 15/20 + 1/20
= 16/20 = 4/5
Bài 3:
a) \(\frac{3}{2}\times\frac{4}{5}\times\frac{2}{3}\) \(=\left(\frac{3}{2}\times\frac{2}{3}\right)\times\frac{4}{5}\)\(=1\times\frac{4}{5}=\frac{4}{5}\)
b) \(\frac{6}{7}\times\left(\frac{5}{3}\times\frac{7}{6}\right)\) \(=\frac{6}{7}\times\frac{35}{18}\)\(=\frac{1\times5}{7\times3}=\frac{5}{21}\)
Bài 4:
a) 2/5 x 1/4 + 3/4 x 2/5
= 2/5 x ( 1/4 + 3/4)
= 2/5 x 1
= 2/5
b) 6/11 : 2/3 +5/11 : 2/3
= ( 6/11 + 5/11) x 3/2
= 11/11 x 3/2
= 1 x 3/2
= 3/2
....
BÀi 1: Thực hiện phép tính ( tính nhanh nếu có thể)
a.\(\left(-\frac{1}{2}\right)-\left(-\frac{3}{5}\right)+\left(-\frac{1}{9}\right)+\frac{1}{71}-\left(-\frac{2}{7}\right)+\frac{4}{35}-\frac{7}{18}\)
b.\(\left(3-\frac{1}{4}+\frac{2}{3}\right)-\left(5-\frac{1}{3}-\frac{6}{5}\right)-\left(6-\frac{7}{4}+\frac{3}{2}\right)\)
c.\(\frac{3}{5}:\left(\frac{-1}{15}-\frac{1}{6}\right)+\frac{3}{5}:\left(\frac{1}{3}-1\frac{1}{15}\right)\)
Tính nhanh:
A=\(\frac{1}{90}-\frac{1}{72}-\frac{1}{56}-\frac{1}{42}-\frac{1}{30}-\frac{1}{20}-\frac{1}{12}-\frac{1}{6}-\frac{1}{2}\)
B=\(\frac{3}{2}-\frac{5}{6}+\frac{7}{12}-\frac{9}{20}+\frac{11}{30}-\frac{13}{42}+\frac{15}{56}-\frac{17}{72}\)
A = \(\frac{-79}{90}\)
B = \(\frac{8}{9}\)
tính giá trị biểu thức
\(A=\frac{-378.132+189.64}{15+18+21+......+45+48}\)
\(B=1,4.\frac{15}{14}-\left(\frac{4}{5}+\frac{2}{5}\right):2\frac{1}{5}-\frac{\frac{73}{77}+\frac{73}{165}+\frac{73}{285}}{\frac{25}{24}+\frac{15}{180}+\frac{20}{285}}\)
\(C=\frac{7+\frac{7}{12}-\frac{7}{144}+\frac{7}{60}}{5+\frac{6}{12}-\frac{5}{144}}.\frac{\frac{3}{4}-\frac{3}{16}+\frac{3}{64}-\frac{3}{256}}{1-\frac{1}{4}+\frac{1}{16}-\frac{1}{34}}-\frac{1}{20}\)