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Đặt \(A=\frac{1}{3}+\frac{1}{3^2}+\frac{1}{3^3}+...+\frac{1}{3^8}\)
\(\Leftrightarrow\)\(3A=1+\frac{1}{3}+\frac{1}{3^2}+...+\frac{1}{3^7}\)
\(\Leftrightarrow\)\(3A-A=\left(1+\frac{1}{3}+\frac{1}{3^2}+...+\frac{1}{3^7}\right)-\left(\frac{1}{3}+\frac{1}{3^2}+\frac{1}{3^3}+...+\frac{1}{3^8}\right)\)
\(\Leftrightarrow\)\(2A=1-\frac{1}{3^8}\)
\(\Leftrightarrow\)\(2A=\frac{3^8-1}{3^8}\)
\(\Leftrightarrow\)\(A=\frac{3^8-1}{3^8}:2\)
\(\Leftrightarrow\)\(A=\frac{3^8-1}{3^8}.\frac{1}{2}\)
\(\Leftrightarrow\)\(A=\frac{3^8-1}{2.3^8}\)
b) Đặt \(A=\frac{1}{3}+\frac{1}{3^2}+\frac{1}{3^3}+.....+\frac{1}{3^8}\)
\(\Rightarrow\)\(3A=1+\frac{1}{3}+\frac{1}{3^2}+....+\frac{1}{3^7}\)
\(\Rightarrow\)\(3A-A=\left(1+\frac{1}{3}+\frac{1}{3^2}+...+\frac{1}{3^7}\right)-\left(\frac{1}{3}+\frac{1}{3^2}+\frac{1}{3^3}+....+\frac{1}{3^8}\right)\)
\(\Rightarrow\)\(2A=1-\frac{1}{3^8}\)
\(\Rightarrow\)\(A=\frac{1-\frac{1}{3^8}}{2}\)
A= 30-(60-(2+(17-12))):15
A=(60-(2+5)):15
A=30-(60-7):15
A=30-53:15
A=30-53/15=397/15
45x16+55x17
=45x16+55x16+55
=16x(45+55)+55
=16x100+55
=1600+55
=1655
Số hạng là: ( 90-12):3+1=27
Tổng: ( 90+12).27:2
= 1377
45 x 48 - 90 x 24 + 1999 = 45 x 48 - 45 x 2 x 24 + 1999
= 45 x 48 - 45 x 48 + 1999
= 0 + 1999
= 1999
Chúc bạn hok tốt nha!
45 x 48 - 90 x 24 + 1999
= 45 x 48 - 45 x 48 + 1999
= 45 x ( 48 - 48 ) + 1999
= 45 x 0 + 1999
= 1999