Lời giải:
$S=(100+99-98-97)+(96+95-94-93)+...+(4+3-2-1)$
$=\underbrace{4+....+4}_{25}=4.25=100$
Lời giải:
$S=(100+99-98-97)+(96+95-94-93)+...+(4+3-2-1)$
$=\underbrace{4+....+4}_{25}=4.25=100$
1 . Tính
B = 1 - 2- 3 + 4 +5 - 6 - 7 + 8+.... + 97 - 98 - 99 + 100
help meeeeeeeee
Tính một cách hợp lý:
a\(\left(\dfrac{1}{2}-1\right)\left(\dfrac{1}{3}-1\right)...\left(\dfrac{1}{100}-1\right)\)) \(x:\dfrac{99}{100}:\dfrac{98}{99}:...:\dfrac{2}{3}:\dfrac{1}{2}\)
b) \(\dfrac{5-\dfrac{5}{3}+\dfrac{5}{9}-\dfrac{5}{27}}{8-\dfrac{8}{3}+\dfrac{8}{9}-\dfrac{8}{27}}:\dfrac{15-\dfrac{15}{11}+\dfrac{15}{121}}{16-\dfrac{16}{11}+\dfrac{16}{121}}\)
c) \(\dfrac{\dfrac{1}{9}-\dfrac{5}{6}-4}{\dfrac{7}{12}-\dfrac{1}{36}-10}\)
d) \(\left(\dfrac{1}{2}+1\right)\left(\dfrac{1}{3}+1\right)...\left(\dfrac{1}{99}+1\right)\)
e)
1+2+3+4+5+6+7+8+9+0+1+2+3+4+5+6+7+8+9+9+8+7+6+5+4+3+2+1+1+34+4+6+7+8+97+6+4+3+32+4+57+7+8+8+6+65+4+3+3+46+7+8+7+64+3+3+5+68+8+6+3+3+5+78+8+6+54+5+7+8+852+3+5+89+8+5+45+7×9×9×9×9×9×9×9×9×9×9×9×8×8×7×9×9×7×7×87×7×8×7×7×8×7×7×8
Bài 1: \(\frac{1}{6}\)+\(\frac{-5}{7}\): x = \(\frac{-7}{18}\)
Bài 2: Tìm tích
a)\(\left(\frac{1}{2}+1\right).\left(\frac{1}{3}+1\right).\left(\frac{1}{4}+1\right)...\left(\frac{1}{999}+1\right)\)
b)\(\left(\frac{1}{2}-1\right).\left(\frac{1}{3}-1\right).\left(\frac{1}{4}-1\right)...\left(\frac{1}{1000}-1\right)\)
c)\(\frac{3}{2^2}.\frac{8}{3^2}.\frac{15}{4^2}...\frac{99}{10^2}\)
1, Tính giá trị các biểu thức sau một cách hợp lí:
a) C = \(\frac{4}{7}.\frac{3}{5}.\frac{7}{4}.\left(-20\right).\frac{5}{6}\)
b) D = \(\left(\frac{81}{121}+\frac{4}{45}-\frac{25}{113}\right).\left(\frac{1}{2}—\frac{1}{3}-\frac{1}{6}\right)\)
2, Tính:
B = \(\frac{2^2}{3}.\frac{3^2}{8}.\frac{4^2}{15}.\frac{5^2}{24}.\frac{6^2}{35}.\frac{7^2}{48}.\frac{8^2}{63}.\frac{9^2}{80}\)
Mọi người giúp e vs ạ, e đg cần gấp. Help me!!!
Chứng tỏ
\(1-\dfrac{1}{2}+\dfrac{1}{3}-\dfrac{1}{4}+...+\dfrac{1}{99}-\dfrac{1}{100}=\dfrac{1}{51}+\dfrac{1}{52}+...+\dfrac{1}{100}\)
a) Cho hai phân số \(\dfrac{1}{n}\) và \(\dfrac{1}{n+1},\left(n\in\mathbb{Z},n>0\right)\). Chứng tỏ rằng tích của hai phân số này bằng hiệu của chúng ?
b) Áp dụng kết quả trên để tính giá trị của các biểu thức sau :
\(A=\dfrac{1}{2}.\dfrac{1}{3}+\dfrac{1}{3}.\dfrac{1}{4}+\dfrac{1}{4}.\dfrac{1}{5}+\dfrac{1}{5}.\dfrac{1}{6}+\dfrac{1}{6}.\dfrac{1}{7}+\dfrac{1}{7}.\dfrac{1}{8}+\dfrac{1}{8}.\dfrac{1}{9}\)
\(B=\dfrac{1}{30}+\dfrac{1}{42}+\dfrac{1}{56}+\dfrac{1}{72}+\dfrac{1}{90}+\dfrac{1}{110}+\dfrac{1}{132}\)
Câu 1 :\(\dfrac{-5}{7}.\dfrac{7}{-45}\);\(\dfrac{-3}{10}.\left(-30\right)\);\(-12.\dfrac{-2}{36}\)
Câu 2: \(\dfrac{3}{4}+\dfrac{1}{8}.\dfrac{-16}{5};\dfrac{7}{15}-\dfrac{18}{21}.\dfrac{7}{9}\)
Câu 3: \(\left(\dfrac{-5}{9}+\dfrac{3}{5}\right).\dfrac{3}{10};\left(\dfrac{3}{9}-\dfrac{2}{5}\right).\dfrac{-3}{10}\)
Câu 4: \(\left(\dfrac{3}{7}+\dfrac{1}{3}\right).\left(\dfrac{1}{8}-\dfrac{1}{2}\right);\left(\dfrac{-9}{12}-\dfrac{16}{30}\right).\left(\dfrac{-18}{22}-\dfrac{6}{11}\right)\)
Càn gấp
B4: Tính nhanh:
a, \(12.\dfrac{-7}{11}.\dfrac{5}{6}.\dfrac{22}{7}\)
b, \(\dfrac{-8}{15}.\dfrac{7}{9}.\dfrac{5}{8}.\left(-18\right)\)
Tính :
a) \(\dfrac{2}{3}+\dfrac{1}{5}.\dfrac{10}{7}\)
b) \(\dfrac{7}{12}-\dfrac{27}{7}.\dfrac{1}{18}\)
c) \(\left(\dfrac{23}{41}-\dfrac{15}{82}\right).\dfrac{41}{25}\)
d) \(\left(\dfrac{4}{5}+\dfrac{1}{2}\right).\left(\dfrac{3}{13}-\dfrac{8}{13}\right)\)