(11x12)+(13x14)+(15x16)+.....+(49x50) bang bao nhiu hehehe
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= 1x2 + 3x2x2 + 5x3x2 + 7x4x2 + 9x5x2 + 11x6x2 + 13x7x2 + 15x8x2
=1x2 + 6x2 + 15 x2 + 28x2 + 45x2 + 66x2 + 91x2 + 120x2
=2 x ( 1+6+15+28+45+66+91+120)
= 2 x 370
=740
=
1x2+3x4+5x6+7x8+9x10+11x12+13x14+15x16
=1x2+3x2x2+5x3x2+7x4x2+9x5x2+11x6x2+13x7x2+15x8x2
=1x2+6x2+15x2+28x2+45x2+66x2+91x2+120x2
= 2x(1+6+15+28+45+66+91+120)
=2x370
=740
\(\frac{5}{10.11}+\frac{5}{11.12}+\frac{5}{12.13}+....+\frac{5}{49.50}\)
\(=5.\left(\frac{1}{10.11}+\frac{1}{11.12}+\frac{1}{12.13}+.....+\frac{1}{49.50}\right)\)
\(=5.\left(\frac{1}{10}-\frac{1}{11}+\frac{1}{11}-\frac{1}{12}+....+\frac{1}{49}-\frac{1}{50}\right)\)
\(=5.\left(\frac{1}{10}-\frac{1}{50}\right)\)
\(=5.\frac{2}{25}\)
\(=\frac{2}{5}\)
5/10 x 11 + 5/11 x 12 + 5/12 x 13 + .... + 5/49 x 50
= 5/10 - 5/11 + 5/11 - 5/12 + 5/12 - 5/13 + ....... + 5/49 - 5/50
= 5/10 - 5/50
= 2/5
\(\frac{5}{11x12}+\frac{5}{12x13}+...+\frac{5}{98x99}\)
=\(\frac{5}{11}-\frac{5}{12}+\frac{5}{12}-\frac{5}{13}+...+\frac{5}{98}-\frac{5}{99}\)
=\(\frac{5}{11}-\frac{5}{99}\)
=\(\frac{40}{99}\)
Cái cuối bỏ 1 số 0 thì đúng hơn nha bạn
\(\frac{5}{11.12}+\frac{5}{12.13}+\frac{5}{13.14}+...+\frac{5}{98.99}\)
\(=5\left(\frac{1}{11.12}+\frac{1}{12.13}+\frac{1}{13.14}+...+\frac{1}{98.99}\right)\)
\(=5\left(\frac{1}{11}-\frac{1}{12}+\frac{1}{12}-\frac{1}{13}+...+\frac{1}{98}-\frac{1}{99}\right)\)
\(=5\left(\frac{1}{11}-\frac{1}{99}\right)\)
\(=5.\frac{8}{99}\)
\(=\frac{40}{99}\)
\(\frac{1}{11x12}+\frac{1}{12x13}+...+\frac{1}{98x99}\)= \(\frac{1}{11}-\frac{1}{12}+\frac{1}{12}-\frac{1}{13}+.....+\frac{1}{98}-\frac{1}{99}\)
= \(\frac{1}{11}-\frac{1}{99}\)
= \(\frac{8}{99}\)
Học tốt !
\(\frac{1}{11\times12}+\frac{1}{12\times13}+\frac{1}{13\times14}+...+\frac{1}{97\times98}+\frac{1}{98\times99}\)
\(=\frac{1}{11}-\frac{1}{12}+\frac{1}{12}-\frac{1}{13}+\frac{1}{13}-\frac{1}{14}+...+\frac{1}{97}-\frac{1}{98}+\frac{1}{98}-\frac{1}{99}\)
\(=\frac{1}{11}-\frac{1}{99}\)
\(=\frac{8}{99}\)