1x5+2x6+3x7+4x8+...+50x54

=(1+2+3+4+...50)x(5+6+7+78+...+54)

=1275x1269=1617975

\(1\cdot5+2\cdot6+\cdots+41\cdot45\)

\(=1\cdot\left(1+4\right)+2\cdot\left(2+4\right)+\cdots+41\cdot\left(41+4\right)\)

\(=\left(1^2+2^2+\cdots+41^2\right)+4\left(1+2+\cdots+41\right)\)

\(=\frac{41\left(41+1\right)\left(2\cdot41+1\right)}{6}+4\cdot\frac{41\cdot42}{2}\)

\(=\frac{41\cdot42\cdot83}{6}+2\cdot41\cdot42=41\cdot7\cdot83+2\cdot41\cdot42=27265\)

Lời giải:

\(\frac{3}{4}\times \frac{8}{9}\times \frac{15}{16}\times ....\times \frac{99}{100}\)

\(=\frac{3\times 8\times 15\times ....\times 99}{4\times 9\times 16\times ....\times 100}\)

\(=\frac{(1\times 3)\times (2\times 4)\times (3\times 5)\times ...\times (9\times 11)}{2\times 2\times 3\times 3\times 4\times 4\times ....\times 10\times 10}\)

\(=\frac{(1\times 2\times 3\times ...\times 9)\times (3\times 4\times 5\times ....\times 11)}{(2\times 3\times 4\times....\times 10)\times (2\times 3\times 4\times ...\times 10)}\)

\(=\frac{1\times 2\times 3\times ....\times 9}{2\times 3\times 4\times ....\times 10}\times \frac{3\times 4\times 5\times ...\times 11}{2\times 3\times 4\times ...\times 10}\)

\(=\frac{1}{10}\times \frac{11}{2}=\frac{11}{20}\)

Ảnh hiển thị bị lỗi hết rồi bạn. Bạn coi lại.

hvt