thực hiện phép tính:
1,1.2+2.3+3.4+....+99.100
2,12+22+32+.....+1992
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b, B = 1.2 + 2.3 + 3.4 + ... + 99.100
3B = 1.2.3 + 2.3.3 + 3.4.3 + ... + 99.100.3
3B = 1.2.3 + 2.3.(4 - 1) + 3.4.(5 - 2) + ... + 99.100.(101 - 98)
3B = 1.2.3 + 2.3.4 - 1.2.3 + 3.4.5 - 2.3.4 + ... + 99.100.101 - 98.99.100
3B = 99.100.101
B = 99.100.101 : 3
B = 333300
a)\(\frac{5}{9}:\left(\frac{1}{11}-\frac{5}{22}\right)+\frac{5}{9}:\left(\frac{1}{15}-\frac{2}{3}\right)\)
\(=\frac{5}{9}:\left[\left(\frac{1}{11}-\frac{5}{22}\right)+\left(\frac{1}{15}-\frac{2}{3}\right)\right]\)
\(=\frac{5}{9}:\left[-\frac{3}{22}+-\frac{3}{5}\right]\)
\(=\frac{5}{9}:\frac{-81}{110}\)
\(=\frac{-550}{729}\)
a: \(=-\left(10x^2+15x-8x-12\right)=-10x^2-7x+12\)
\(3^2\cdot5+2^3\cdot10-3^4:3\\ =9\cdot5+8\cdot10-3^4\\ =45+80-27\\ =98\)
\(3^2.5+2^3.10-3^4:3\)
\(=9.5+8.10-3^3\)
\(=45+80-27\)
\(=125-27\)
\(=98\)
\(#WendyDang\)
a, (y-476)x2=2196x3
(y-476)x2=2196x2+2196
(y-476)x2-2196x2=2196
(y-476-2196)x2=2196
(y-(476+2196)x2=2196
(y-2672)x2=2196
(y-2672)x2=1098x2
(y-2672)x2-1098x2=0
(y-2672-1098)x2=0
(y-(2672+1098)x2=0
(y-3770)x2=0
y-3770=0
y=3770
ĐS: y=3770
\(60-\left[15.2+\left(4+1^{35}\right)^2\right]\)
\(\Rightarrow60-\left[30+\left(4+1\right)^2\right]\)
\(\Rightarrow60-\left[30+25\right]\)
\(\Rightarrow60-55\)
\(\Rightarrow5\)
\(A=1.2+2.3+3.4+...+99.100\)
\(3A=1.2.3+2.3.\left(4-1\right)+3.4.\left(5-2\right)+...+99.100.\left(101-98\right)\)
\(3A=99.100.101\)
\(A=33.100.101=333300\)
\(B=1^2+2^2+3^2+...+199^2\)
\(=1.2-1+2.3-2+3.4-3+...+199.200-199\)
\(=\left(1.2+2.3+3.4+...+199.200\right)-\left(1+2+3+...+199\right)\)
\(=\frac{199.200.201}{3}-\frac{\left(1+199\right).199}{2}\)
\(=2666600-19900=2646700\)