phan h cac so tren ra roi nhan lai la dc xin loi nha may binh bi liet nen ko giai dc
\(P=\frac{4}{3}.\frac{9}{8}.\frac{16}{15}.....\frac{10000}{9999}=\frac{2.2}{1.3}.\frac{3.3}{2.4}.\frac{4.4}{3.5}....\frac{100.100}{99.101}\)
\(=\frac{\left(2.3....100\right).\left(2.3.4...100\right)}{\left(1.2.3.4...99\right).\left(3.4.....101\right)}=\frac{100.2}{101}=\frac{200}{101}\)
算:4/3*9/8*16/15*25/24*.*9801/989992014-12-1+2+3+4+5+6+7+8+9+10.+9999+100=（）
9999+999+99+9 9999×2222+3333×3334 10000-1-2-3-4-...-80 1+2+3+4+...+78+79+80 2007*2005/2000 要简算
1+2+3+4+5+6+.+9999+10000=
10000-9999+9998-9997…+6-5+4-3+2-1等于多少
=(2/1*3)*(3平方/2*4)*(4/3*5)*(5平方/4*6)................*(99平方/98*100)*(100平方/99*101)
=2*100/101=200/101
\(p=\frac{2\cdot2}{1\cdot3}\cdot\frac{3\cdot3}{2\cdot4}\cdot\frac{4\cdot4}{3\cdot5}\cdot........\cdot\frac{100\cdot100}{99\cdot101}\)
\(p=\frac{2\cdot3\cdot4\cdot...\cdot100}{1\cdot2\cdot3\cdot...\cdot99}\cdot\frac{2\cdot3\cdot4\cdot...\cdot100}{3\cdot4\cdot5\cdot...\cdot101}\)
\(p=\frac{2}{1}\cdot\frac{100}{101}\)
\(p=\frac{200}{101}\)
\(P=\frac{4}{3}.\frac{9}{8}.\frac{16}{15}......\frac{10000}{9999}\)
\(P=\frac{2.2}{1.3}.\frac{3.3}{2.4}.\frac{4.4}{3.5}.....\frac{100.100}{99.101}\)
\(P=\frac{2.3.4...100}{1.2.3....99}.\frac{2.3.4....100}{3.4.5....101}\)
\(P=100.\frac{2}{101}=\frac{200}{101}\)
Vay \(P=\frac{200}{101}\)
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Ta có:
\(P=\frac{4}{3}\times\frac{9}{8}\times\frac{16}{15}\times...\times\frac{10000}{9999}\)
\(=\frac{2\times2}{3}\times\frac{3\times3}{2\times4}\times\frac{4\times4}{3\times5}\times...\times\frac{100\times100}{99\times101}\)
\(=\frac{2\times2\times3\times3\times4\times4\times...\times100\times100}{3\times2\times4\times3\times5\times...\times99\times101}\)
\(=\frac{\left(2\times3\times4\times...\times100\right)\times\left(2\times3\times4\times...\times100\right)}{\left(2\times3\times4\times...\times99\right)\times\left(3\times4\times5\times...\times101\right)}\)
\(=\frac{2}{101}\)
Vậy \(P=\frac{2}{101}\)