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45- { [(120-60):15+5]:3} + (-55)
= 45 - { [60:15+5]:3} + (-55)
= 45 - {9:3} +(-55)
= 45 - 3 + (-55) = -13
b) \(6^2-2^3.5^0.6=36-8.1.6\)
\(36-48=-12\)
TICK MIK NHA
(0.6)^5/(0.2)^6
= [(0.2)^5. 3^5]/(0.2)^6
= 3^5/0.2
=243/0.2
= 1215
6^3+3.6^2+3^3/-13
= 2^3.3^3+3.2^2.3^2+3^3/-13
=3^3(2^3+2^2+1)/-13
=3^3.13/-13
=-27
\(\frac{6^3+3\cdot6^2+3^3}{-13}=\frac{\left(3\cdot2\right)^3+3\cdot\left(3\cdot2\right)^2+3^3}{-13}=\frac{3^3\cdot2^3+3\cdot3^2\cdot2^2+3^3}{-13}=\frac{3^3\cdot\left(2^3+2^2+1\right)}{-13}=\frac{27\cdot13}{-13}=-27\)
c) \(3^2+2^4-\left(6^8:6^6-6^2\right)< 5^x< 125\)
\(=9+16-\left(6^{8-6}-36\right)< 5^x< 5^3\)
\(=25-\left(6^2-36\right)< 5^x< 5^3\)
\(=25-\left(36-36\right)< 5^x< 5^3\)
\(=25-0< 5^x< 5^3\)
\(=25< 5^x< 5^3\)
\(=5^2< 5^x< 5^3\)
Vì \(5^2=25\) và \(5^3=125\) nên \(x\) không thể thỏa mãn đề bài
⇒ \(x\) không thỏa mãn đề bài
\(B=136.25+75.136-6^2.10^2\)
\(=136.\left(75+25\right)-36.100\)
\(=136.100-36.100\)
\(=\left(136-36\right).100\)
\(=100.100=10000\)
\(C=2^3.5^3-\left\{7^2.2^3.5^2.\left[4^3:8+11^2:121-2\left(37-5.7\right)\right]\right\}\)
\(=10^3-\left\{49.8.25.\left[8+1+2.2\right]\right\}\)
\(=1000-\left(49.200.13\right)\)
\(=1000-127400\)
\(=-126400\)
Bài này đơn giản thôi bạn
B= 136.(25+75)-36.100
B= 136. 100-36.100
B= 100.(136-36)
B= 100.100
B= 10000
Em xem lại đề câu B nhé\(B=\dfrac{3}{2}+\dfrac{3}{6}+\dfrac{3}{12}+\dfrac{3}{20}+...+\dfrac{3}{\left(n-1\right).n}\\ =3.\left(\dfrac{1}{1.2}+\dfrac{1}{2.3}+\dfrac{1}{3.4}+\dfrac{1}{4.5}+...+\dfrac{1}{\left(n-1\right).n}\right)\\ =3.\left(1-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+...+\dfrac{1}{n-1}-\dfrac{1}{n}\right)=3.\left(1-\dfrac{1}{n}\right)=3.\dfrac{n-1}{n}=3-\dfrac{3}{n}.\)
\(C=\dfrac{2}{1.3}+\dfrac{2}{3.5}+...+\dfrac{2}{30.32}\\ =1-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{5}+...+\dfrac{1}{30}-\dfrac{1}{32}\\ =1-\dfrac{1}{32}=\dfrac{31}{32}.\)
\(D=\dfrac{1}{2}.\left(1-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{5}+...+\dfrac{1}{n+1}-\dfrac{1}{n+3}\right)\\ =\dfrac{1}{2}.\left(1-\dfrac{1}{n+3}\right)=\dfrac{1}{2}.\dfrac{n+2}{n+3}.\)
b)
\(\frac{2}{3.5}+\frac{2}{5.7}+......+\frac{2}{97.99}\)
\(=\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+.....+\frac{1}{97}-\frac{1}{99}\)
\(=\frac{1}{3}-\frac{1}{99}\)
\(=\frac{32}{99}\)
c)
\(\frac{7}{3.4}+\frac{7}{4.5}+.....+\frac{7}{60.61}\)
\(=7\left(\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+.....+\frac{1}{60}-\frac{1}{61}\right)\)
\(=7\left(\frac{1}{3}-\frac{1}{61}\right)\)
\(=\frac{406}{183}\)
d)
\(\frac{6}{2.4}+\frac{6}{4.6}+....+\frac{1}{72.74}\)
\(=3\left(\frac{1}{2}-\frac{1}{4}+\frac{1}{4}-\frac{1}{6}+.....+\frac{1}{72}-\frac{1}{74}\right)\)
\(=3\left(\frac{1}{2}-\frac{1}{74}\right)\)
=57/37
A = 1 /1.2 + 1/ 2.3 + 1 /3.4 + . . . + 1/ 49.50 + 1/ 50.51
A = 2 − 1/ 1.2 + 3 − 2 /2.3 + 4 − 3 /3.4 + . . . + 50 − 49 /49.50 + 51 − 50/ 50.51
A = 1 − 1/ 2 + 1/ 2 − 1 /3 + 1 /3 − 1/ 4 + . . . + 1 /50 − 1 /51
A=1-1/51
A=50/51