Cho A = 1 + 2 + 2² + 2³ + ... + 2²⁰⁰⁸

->  2A = 2 + 2² + 2³ + 2⁴ +...+ 2²⁰⁰⁹ 

-> 2A - A = (  2 + 2² + 2³ + 2⁴ +...+ 2²⁰⁰⁹ ) - ( 1 + 2 + 2² + 2³ + ... + 2²⁰⁰⁸ )

->       A = \(2^{2009}-1=-\left(1-2^{2009}\right)\)

S =  \(\frac{-\left(1-2^{2009}\right)}{1-2^{2009}}\)=-1

\(A=\frac{3}{4}.\frac{8}{9}.\frac{15}{16}...\frac{399}{400}\Rightarrow A=\frac{1.3}{2.2}.\frac{2.4}{3.3}.\frac{3.5}{4.4}...\frac{19.21}{20.20}\Rightarrow\frac{1.2.3...19}{2.3.4...20}.\frac{3.4.5...21}{2.3.4...20}\) \(\Rightarrow A=\frac{1}{20}.\frac{21}{2}=\frac{21}{40}\)

Sửa đê, toán 6.

\(A=\left(\frac{1}{4}-1\right)\left(\frac{1}{9}-1\right)\left(\frac{1}{16}-1\right)...\left(\frac{1}{400}-1\right)\)

\(-A=\left(1-\frac{1}{4}\right)\left(1-\frac{1}{9}\right)\left(1-\frac{1}{16}\right)...\left(1-\frac{1}{400}\right)\)

\(-A=\frac{3}{4}\cdot\frac{8}{9}\cdot\frac{15}{16}\cdot...\cdot\frac{399}{400}\)

\(-A=\frac{1\cdot3}{2\cdot2}\cdot\frac{2.4}{3.3}\cdot\frac{3.5}{4.4}\cdot...\cdot\frac{19.21}{20.20}\)

\(-A=\frac{1\cdot2\cdot3\cdot...\cdot19}{2\cdot3\cdot4\cdot...\cdot20}\cdot\frac{3\cdot4\cdot5\cdot...\cdot21}{2\cdot3\cdot4\cdot...\cdot20}\)

\(-A=\frac{1}{20}\cdot\frac{21}{2}=\frac{21}{40}>\frac{20}{40}=\frac{1}{2}\)

\(-A>\frac{1}{2}\Rightarrow A< \frac{1}{2}\)

- Cảm ơn mặc dù mình mới tự giải được ><

\(A=\frac{2.3.5+4.9.25+6.9.35+10.21.40}{2.3.7+4.9.35+6.9.49+10.21.56}\)

\(A=\frac{\left(2.3.5\right)+\left(2.3.5\right).2.3.5+\left(2.3.5\right).3.3.7+\left(2.3.5\right).5.7.8}{\left(2.3.7\right)+\left(2.3.7\right).2.3.5+\left(2.3.7\right).3.3.7+\left(2.3.7\right).5.7.8}\)

\(A=\frac{\left(2.3.5\right).\left(1+2.3.5+3.3.7+5.7.8\right)}{\left(2.3.7\right).\left(1+2.3.5+3.3.7+5.7.8\right)}\)

\(A=\frac{2.3.5}{2.3.7}=\frac{5}{7}.\)

\(B=\left(-\frac{3}{4}\right).\left(-\frac{8}{9}\right).\left(-\frac{15}{16}\right)...\left(-\frac{399}{400}\right)\)

\(B=-\frac{1.3.2.4.3.5...19.21}{2.2.3.3.4.4...20.20}\)

\(B=-\frac{1.2.3...19.3.4.5...21}{2.3.4...20.2.3.4...20}=-\frac{21}{40}.\)

chịu lun nhưng cho tao nha