Question

cho A=1/2+3/2+(3/2)^2+.....+(3/2)^2012, B=(3/2)^2013:2. tính B-A

Answer 1

\(\frac{3}{2}.A=\frac{3}{4}+\left(\frac{3}{2}\right)^2+\left(\frac{3}{2}\right)^3+...+\left(\frac{3}{2}\right)^{2013}\)

\(\Rightarrow\frac{3}{2}.A-A=\frac{3}{4}+\left(\frac{3}{2}\right)^2+\left(\frac{3}{2}\right)^3+...+\left(\frac{3}{2}\right)^{2013}-\left(\frac{1}{2}+\frac{3}{2}+\left(\frac{3}{2}\right)^2+...+\left(\frac{3}{2}\right)^{2012}\right)\)

\(\Rightarrow\frac{1}{2}.A=\frac{3}{4}+\left(\frac{3}{2}\right)^{2013}-\frac{1}{2}-\frac{3}{2}=\left(\frac{3}{2}\right)^{2013}-\frac{5}{4}\Rightarrow A=2.\left(\frac{3}{2}\right)^{2013}-\frac{5}{2}\)

\(B-A=\frac{1}{2}.\left(\frac{3}{2}\right)^{2013}-2.\left(\frac{3}{2}\right)^{2013}+\frac{5}{2}=-\left(\frac{3}{2}\right)^{2014}+\frac{5}{2}\)

Answer 2

Trần Thị Loan tại sao lại + 5/2?

Answer 3

ngu thế Bụng Mon

Answer 4

5/4 ở đâu vậy bạn .Mình học ko giỏi xin giải đáp

Answer 5

Loan sai chỗ cuối

Answer 6

3​.A=43​+(23​)2+(23​)3+...+(23​)2013

⇒32.�−�=34+(32)2+(32)3+...+(32)2013−(12+32+(32)2+...+(32)2012)⇒23​.A−A=43​+(23​)2+(23​)3+...+(23​)2013−(21​+23​+(23​)2+...+(23​)2012)

⇒12.�=34+(32)2013−12−32=(32)2013−54⇒�=2.(32)2013−52⇒21​.A=43​+(23​)2013−21​−23​=(23​)2013−45​⇒A=2.(23​)2013−25​

�−�=12.(32)2013−2.(32)2013+52=−(32)2014+52B−A=21​.(23​)2013−2.(23​)2013+25​=−(23​)2014+25​