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a) \(A=1+2+2^2+...+2^{50}\)
\(\Rightarrow2A=2+2^2+...+2^{51}\)
\(\Rightarrow A=2A-A=2+2^2+...+2^{51}-1-2-2^2-...-2^{50}=2^{51}-1\)
b) \(B=1+3+3^2+...+3^{100}\)
\(\Rightarrow3B=3+3^2+...+3^{101}\)
\(\Rightarrow2B=3B-B=3+3^2+...+3^{101}-1-3-3^2-...-3^{100}=3^{101}-1\)
\(\Rightarrow B=\dfrac{3^{101}-1}{2}\)
c) \(C=5+5^2+...+5^{30}\)
\(\Rightarrow5C=5^2+5^3+...+5^{31}\)
\(\Rightarrow4C=5C-C=5^2+5^3+...+5^{31}-5-5^2-...-5^{30}=5^{31}-5\)
\(\Rightarrow C=\dfrac{5^{31}-5}{4}\)
d) \(D=2^{100}-2^{99}+2^{98}-...+2^2-2\)
\(\Rightarrow2D=2^{101}-2^{100}+2^{99}-...+2^3-2^2\)
\(\Rightarrow3D=2D+D=2^{101}-2^{100}+2^{99}-...+2^3-2^2+2^{100}-2^{99}+...+2^2-2=2^{101}-2\)
\(\Rightarrow D=\dfrac{2^{101}-2}{3}\)
a/ 3 + 2387 : 77 - 33
= 3 + 31 - 33
= 31 + ( 3 - 33)
= 31 + (-30)
= 1
b/ 8 x 33 x 25 x 125 x 4
= (8 x 125) x (4 x 25) x 33
= 1000 x 100 x 33
= 100000x 33
= 3300000
c/ 20, 16 : 0,01
= 2016 : 1
= 2016
Thêm :
D, 8,6 - 2,75
E, 4\(\frac{3}{8}\)+ 5\(\frac{2}{3}\)
F, 3\(\frac{1}{5}\)- 1\(\frac{1}{5}\)+ \(\frac{2}{5}\)
G, \(\frac{2}{5}\)+ \(\frac{3}{5}\): \(\frac{4}{5}\)
H, \(\frac{5}{2}\)x \(\frac{1}{3}\)+ \(\frac{1}{4}\)
\(a,\left(-14\right)\cdot\left(-125\right)\cdot\left(+3\right)\cdot\left(-8\right)\\ =\left[\left(-125\right)\cdot\left(-8\right)\right]\cdot\left[3\cdot\left(-14\right)\right]\\ =1000\cdot\left(-42\right)\\ =-42000\)
Xem lại đề câu b nhé
\(D=2^{100}-2^{99}-2^{98}-...-2^2-2-1\\ =2^{100}-\left(2^{99}+2^{98}+...+2^2+2+1\right)\\ \text{Đặt }G=2^{99}+2^{98}+...+2^2+2+1\\ 2G=2^{100}+2^{99}+...+2^3+2^2+2\\ 2G-G=\left(2^{100}+2^{99}+...+2^3+2^2+2\right)-\left(2^{99}+2^{98}+...+2^2+2+1\right)\\ G=2^{100}-1\\ D=2^{100}-G\\ =2^{100}-\left(2^{100}-1\right)\\ =2^{100}-2^{100}+1\\ =1\)
b/(-25).34.2+/(-34).(-250)/
=(-50).34+34.250
=34.(-50+250)
=34.200
=6800