biết a = 1.2+2.3+3.4+.....+99.100=333300 thì B = 1.4+2.5+3.6+....+99.102=......
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biết A = 1.2+2.3+3.4+.........+99.100=333300 thì B = 1.4+2.5+3.6+......+99.102 = .....
\(B=1.4+2.5+3.6+...+99.102\)
\(=1.\left(2+2\right)+2.\left(2+3\right)+3.\left(2+4\right)+...+99.\left(2+100\right)\)
\(=1.2+2.1+2.3+2.2+3.4+2.3+...+99.100+2.99\)
\(=\left(1.2+2.3+...+99.100\right)+\left(2.1+2.2+2.3+...+2.99\right)\)
\(=333300+2.\left(1+2+3+...+99\right)\)
\(=333300+2.\left(\frac{99.100}{2}\right)\)
\(=333300+99.100=333300+9900=343200\)
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Biết A=1.2+2.3+3.4......+99.100=333300 thì B=1.4+2.5+3.6..+99.102= ?
Biết A=1.2+2.3+3.4+...+99.100=333300 thì B=1.4+2.5+3.6+...+ 99.102=?
B-A=1.(4-2)+2.(5-3)+...+99.(102-100)
B-A=2.(1+2+...+99)
B-A=\(\frac{\left(99+1\right).99}{2}\)
B-A=4950
B=333300+4950=338250
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Biết \(A=1.2+2.3+3.4+...+99.100=333300\) thì \(B=1.4+2.5+3.6+...+99.102=...\)
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Tính tổng:
a) 1.2 + 2.3 + 3.4 + ... + 99.100
b) 1.3 + 2.4 + 3.5 + ... + 99.101
c) 1.4 + 2.5 + 3.6 + ... + 99.102
Rút gọn:
\(\frac{1.4+2.5+3.6+4.7+...+99.102}{1.2+2.3+3.4+4.5+...+99.100}\)
a,
1.2+2.3+3.4+...+99.100
b,
1.3+2.4+3.5+...+99.101
c,
1.4+2.5+3.6+...+99.102
d,
1.2.3+2.3.4+3.4.5+...+98.99.100
Tính:
a,A=1.2+2.3+3.4+......+99.100
b,B=1.3+2.4+3.5+......+99.101
c,C=1.4+2.5+3.6+......+99.102
d,D=1.2.3+2.3.4+3.4.5+.......+98.99.100
\(A=1.2+2.3+3.4+...+99.100\)
\(\Rightarrow3A=1.2.3+2.3\left(4-1\right)+3.4\left(5-2\right)+...+90.100\left(101-98\right)\)
\(\Rightarrow3A=1.2.3+2.3.4-1.2.3+3.4.5-2.3.4+...+99.100.101-98.99.100\)
\(\Rightarrow3A=99.100.101\)
\(\Rightarrow A=\left(99.100.101\right):3\)
\(\Rightarrow A=333300\)
\(B=1.3+2.4+3.5+...+99.101\)
\(\Rightarrow B=1\left(2+1\right)+2\left(3+1\right)+3\left(4+1\right)+...+99\left(100+1\right)\)
\(\Rightarrow B=1.2+1+2.3+2+3.4+3+...+99.100+99\)
\(\Rightarrow B=\left(1.2+2.3+3.4+...+99.100\right)+\left(1+2+3+...+99\right)\)
\(\Rightarrow B=333300+4950\)
\(\Rightarrow B=338250\)
\(D=1.2.3+2.3.4+3.4.5+...+98.99.100\)
\(\Rightarrow4D=1.2.3.4+2.3.4.4+...+98.99.100.4\)
\(\Rightarrow4D=1.2.3\left(4-0\right)+2.3.4\left(5-1\right)+...+98.99.100\left(101-97\right)\)
\(\Rightarrow4D=1.2.3.4-0.1.2.3+2.3.4.5-1.2.3.4+...+98.99.100-97.98.99\)
\(\Rightarrow4D=98.99.100\)
\(\Rightarrow D=\left(98.99.100\right):4=242550\)
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Tính:
f) F= 1.2+2.3+3.4+...+n(n+1)
g) G= 1.2.3+2.3.4+3.4.5+...+99.100.101
h) H= 1.2.3+2.3.4+3.4.5+...+n(n+1)(n+2)
i) I= 1.3+2.4+3.5+...+99.100
j) J= 1.4+2.5+3.6+...+99.102