tính
\(\left(-1\frac{1}{2}\right).\left(-1\frac{1}{3}\right)...\left(-1\frac{1}{99}\right)\)
K
Khách
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21 tháng 10 2016
\(\left(100+\frac{99}{2}+\frac{98}{3}+...+\frac{1}{100}\right):\left(\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+...+\frac{1}{101}\right)-2\)-2
=\(\left[\left(\frac{99}{2}+1\right)+\left(\frac{98}{3}+1\right)+...+\left(\frac{1}{100}+1\right)+1\right]:\left(\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+...+\frac{1}{101}\right)-2\)
=\(\left(\frac{101}{2}+\frac{101}{3}+\frac{101}{4}+....+\frac{101}{100}+\frac{101}{101}\right):\left(\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+...+\frac{1}{101}\right)-2\)
=\(101\left(\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+...+\frac{1}{101}\right):\left(\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+...+\frac{1}{101}\right)-2\)
=99
KB
26 tháng 3 2019
1, A=\(\frac{3}{2}.\frac{4}{3}.\frac{5}{4}....\frac{100}{99}\)
A= \(\frac{100}{2}\)
A=50
2, B=\(\frac{-1}{2}.\frac{-2}{3}....\frac{-98}{99}\)
B= \(\frac{1}{99}\)
HN
26 tháng 3 2019
\(A=\left(\frac{1}{2}+1\right)\cdot\left(\frac{1}{3}+1\right)\cdot\left(\frac{1}{4}+1\right)......\left(\frac{1}{99}+1\right)\)
\(=\frac{3}{2}\cdot\frac{4}{3}\cdot\frac{5}{4}......\frac{99}{98}\cdot\frac{100}{99}\)
\(=\frac{100}{2}\)
\(=50\)
\(B=\left(\frac{1}{2}-1\right)\cdot\left(\frac{1}{3}-1\right)\cdot\left(\frac{1}{4}-1\right)......\left(\frac{1}{99}-1\right)\)
\(=\left(-\frac{1}{2}\right)\cdot\left(-\frac{2}{3}\right)\cdot\left(-\frac{3}{4}\right).....\left(-\frac{97}{98}\right)\cdot\left(-\frac{98}{99}\right)\)
\(=-\frac{1}{99}\)
Ta có: \(\left(99-2\right)+1=98\)
\(\Rightarrow\)Có 98 thừa số nên tích mang dấu \(+\)
\(\Rightarrow\)Ta có:\(1\frac{1}{2}.1\frac{1}{3}....1\frac{1}{99}\)
\(=\frac{3}{2}.\frac{4}{3}...\frac{100}{99}\)
\(=\frac{3.4.5...100}{2.3.4...99}\)
\(=\frac{100}{2}=50\)
\(\left(-1\frac{1}{2}\right)\)\(.\)\(\left(-1\frac{1}{3}\right)\)\(...\)\(\left(-1\frac{1}{99}\right)\)
\(=\)\(\left(\frac{-3}{2}\right)\)\(.\)\(\left(\frac{-4}{3}\right)\)\(...\)\(\left(\frac{-100}{99}\right)\)
\(=\)\(\left\{\frac{\left(-3\right).\left(-4\right)...\left(-100\right)}{2.3...99}\right\}\)
\(=\)\(\frac{-100}{2}\)
\(=\)\(-50\)
\(k\)\(cho\)\(mình\)\(nha\)