#)Giải :
\(\frac{1}{100.99}-\frac{1}{99.98}-\frac{1}{98.97}-...-\frac{1}{3.2}-\frac{1}{2.1}\)
\(=-\left(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+... +\frac{1}{99.100}\right)\)
\(=-\left(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{99}-\frac{1}{100}\right)\)
\(=-\left(1-\frac{1}{100}\right)\)
\(=-\frac{99}{100}\)
#~Will~be~Pens~#
\(\frac{1}{100\cdot99}-\frac{1}{99\cdot98}-\frac{1}{98\cdot97}-...-\frac{1}{3\cdot2}-\frac{1}{2\cdot1}\)
\(=-\left[\frac{1}{1\cdot2}+\frac{1}{2\cdot3}+\frac{1}{3\cdot4}+...+\frac{1}{98\cdot99}+\frac{1}{99\cdot100}\right]\)
\(=-\left[1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{99}-\frac{1}{100}\right]\)
\(=-\left[1-\frac{1}{100}\right]=-\frac{99}{100}\)
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bạn tham khảo nhé:
https://olm.vn/hoi-dap/detail/10005362177.html
https://olm.vn/hoi-dap/detail/10005362177.html
thanks
bạn tham khảo nhé:
https://olm.vn/hoi-dap/detail/10005362177.html
https://olm.vn/hoi-dap/detail/10005362177.html
thanks
\(\frac{1}{100.99}-\frac{1}{99.98}-\frac{1}{98.97}-...-\frac{1}{3.2}-\frac{1}{2.1}\)
=\(\frac{1}{100.99}-\left(\frac{1}{99.98}+\frac{1}{98.97}+...+\frac{1}{3.2}+\frac{1}{2.1}\right)\)
= \(\frac{1}{100.99}-\left(\frac{1}{2.1}+\frac{1}{3.2}+...\frac{1}{97.98}+\frac{1}{98.99}\right)\)
=\(\frac{1}{100.99}-\left(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{97}-\frac{1}{98}+\frac{1}{98}-\frac{1}{99}\right)\)
= \(\frac{1}{9900}-\left(1-\frac{1}{99}\right)\)
= \(\frac{1}{9900}-\frac{98}{90}\)
=\(\frac{1}{9900}-\frac{9800}{9900}\)
= \(\frac{-9799}{9900}\)
- Study well -
1/100*99 - 1/99*98 - 1/98*97 - .... - 1/3*2 - 1/2*1
= 1/100*99 - (1/1*2 + 1/2*3 + 1/3*4 + ... + 1/98*99)
= 1/9900 - (1 - 1/2 + 1/2 - 1/3 + 1/3 - 1/4 + ... + 1/98 - 1/99)
= 1/9900 - (1 - 1/99)
= 1/9900 - 98/99
= ...
\(\frac{1}{100.99}-\frac{1}{99.98}-\frac{1}{98.97}-...-\frac{1}{3.2}-\frac{1}{2.1}\)
\(=\frac{1}{100.99}-\left(\frac{1}{99.98}+\frac{1}{98.97}+...+\frac{1}{3.2}+\frac{1}{2.1}\right)\)
\(=\frac{1}{100.99}-\left(\frac{1}{1.2}+\frac{1}{2.3}+...+\frac{1}{97.98}+\frac{1}{98.99}\right)\)
\(=\frac{1}{100.99}-\left(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{97}-\frac{1}{98}+\frac{1}{98}-\frac{1}{99}\right)\)
\(=\frac{1}{9900}-\left(1-\frac{1}{99}\right)\)
\(=\frac{1}{9900}-\frac{98}{99}\)
\(=\frac{1}{9900}-\frac{9800}{9900}\)
\(=\frac{-9799}{9900}\)