tính giá trị biểu thức=1x5+2x6+3x7+4x8+...............+21x25
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1x5+2x6+3x7+4x8+...+50x54
=(1+2+3+4+...50)x(5+6+7+78+...+54)
=1275x1269=1617975
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Lời giải:
\(\frac{3}{4}\times \frac{8}{9}\times \frac{15}{16}\times ....\times \frac{99}{100}\)
\(=\frac{3\times 8\times 15\times ....\times 99}{4\times 9\times 16\times ....\times 100}\)
\(=\frac{(1\times 3)\times (2\times 4)\times (3\times 5)\times ...\times (9\times 11)}{2\times 2\times 3\times 3\times 4\times 4\times ....\times 10\times 10}\)
\(=\frac{(1\times 2\times 3\times ...\times 9)\times (3\times 4\times 5\times ....\times 11)}{(2\times 3\times 4\times....\times 10)\times (2\times 3\times 4\times ...\times 10)}\)
\(=\frac{1\times 2\times 3\times ....\times 9}{2\times 3\times 4\times ....\times 10}\times \frac{3\times 4\times 5\times ...\times 11}{2\times 3\times 4\times ...\times 10}\)
\(=\frac{1}{10}\times \frac{11}{2}=\frac{11}{20}\)
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