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A = 1.2 + 2.3 + 3.4 + ... + 99.100
3A = 1.2.3 + 2.3.3 + 3.4.3 + ... + 99.100.3
3A = 1.2.(3 - 0) + 2.3.(4 - 1) + 3.4.(5 - 2) +...+ 99.100.(101-98)
3A = 1.2.3 - 0 + 2.3.4 - 1.2.3 + 3.4.5 - 2.3.4 + ... + 99.100.101 - 98.99.100
3A = 99.100.101
A = 333300
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\(\dfrac{1}{1\cdot2}+\dfrac{1}{2\cdot3}+\dfrac{1}{3\cdot4}+\dfrac{1}{4\cdot5}+\dfrac{1}{5\cdot6}+\dfrac{1}{6\cdot7}\)
\(=1-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{6}+\dfrac{1}{6}-\dfrac{1}{7}\)
\(=1+0+0+0+0+0-\dfrac{1}{7}\)
\(=1-\dfrac{1}{7}\)
\(=\dfrac{7}{7}-\dfrac{1}{7}\)
\(=\dfrac{6}{7}\)
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\(a,\frac{15^{33}}{15^{32}.15}=\frac{15^{33}}{15^{33}}=1\)
\(b,6.25.4+3.27.8+96.12\)
\(=6.4.25+3.8.27+24.4.12\)
\(=24.25+24.27+24.48\)
\(=24.\left(25+27+48\right)\)
\(=24.100\)
\(=2400\)
3.27.8+2.39.12+4.34.6
=(3.8).27+(12.2).39+(4.6).34
=24.27+24.39+24.34
=24.(27+39+34)
=24.100
=2400
3.27.8+2.39.12+4.34.6
=3.8.27+2.12.39+4.6.34
=24.27+24.39+24.34
=24.(27+39+34)
=24.100=2400