C= 1/100 -1/100×99 -1/99×98 -1/98×97-...-1/3×2 - 1/2×1
Những câu hỏi liên quan
C=1/100 - 1/100*99 - 1/99*98 - 1/98*97 - . . . -1/3*2 - 1/2*1
\(\Rightarrow C=\frac{1}{100}-\left(\frac{1}{100\cdot99}+\frac{1}{99\cdot98}+\frac{1}{98\cdot97}+...+\frac{1}{3\cdot2}+\frac{1}{2\cdot1}\right)\)
\(\Rightarrow C=\frac{1}{100}-\left(\frac{1}{1\cdot2}+\frac{1}{2\cdot3}+...+\frac{1}{98\cdot99}+\frac{1}{99\cdot100}\right)\)
\(\Rightarrow C=\frac{1}{100}-\left(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{98}-\frac{1}{99}+\frac{1}{99}-\frac{1}{100}\right)\)
\(\Rightarrow C=\frac{1}{100}-\left(1-\frac{1}{100}\right)\)
\(\Rightarrow C=\frac{1}{100}-1+\frac{1}{100}\)
\(\Rightarrow C=\left(\frac{1}{100}+\frac{1}{100}\right)-1\)
\(\Rightarrow C=\frac{1}{50}-1\)
\(\Rightarrow C=\frac{-49}{50}\)
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-1 / 100 . 99 - 1 / 99 . 98 - 1 / 98 . 97 - ... -1 / 3 . 2 - 1 / 2 . 1
Vậy bạn làm như thế nào? Chỉ mình đi
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Tính:1:99/100:98/99:97/98:....:2/3:1/2
Tính nhanh
a, 1-2+3-4+.....+2015-2016+2017
b,1+3-5-7+9+11+....+97-98-99+100+101
c,1-2-3+4+5-6-7+....+97-98-99+100+101
d,2^100-2^99-2^98-....-2-1
Nhanh nha m dang cần gấp
99/1+98/2+97/3+................+2/98+1/99
1/2+1/3+1/4+.......................+1/99+1/100
C=(1/2+1/3+ 1/4+... +1/100): (99/1 + 98/2 + 97/3 ... +1/99)
tìm C
Ta có: \(\frac{99}{1}+\frac{98}{2}+\cdots+\frac{1}{99}\)
\(=\left(1+\frac{98}{2}\right)+\left(1+\frac{97}{3}\right)+\cdots+\left(1+\frac{1}{99}\right)+1\)
\(=\frac{100}{2}+\frac{100}{3}+\cdots+\frac{100}{99}+\frac{100}{100}\)
\(=100\left(\frac12+\frac13+\cdots+\frac{1}{100}\right)\)
Ta có: \(C=\frac{\frac12+\frac13+\frac14+\cdots+\frac{1}{100}}{\frac{99}{1}+\frac{98}{2}+\cdots+\frac{1}{99}}\)
\(=\frac{\frac12+\frac13+\cdots+\frac{1}{100}}{100\left(\frac12+\frac13+\cdots+\frac{1}{100}\right)}=\frac{1}{100}\)
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1)11-12+13-14+15-16+17-18+19-20+21-22+.........+99-100
2)2-4+6-8+......+1998-2000
3)-1+3-5+7-....+97-99
4)1+2-3-4+.........+97+98-99-100
5)1-2+3-4+.............+99-100
6)1+3-5-7+......+97-98-99+100
7)2100-299-298-..........22-2-1
8)1-4+7-10+........+307-310+313
Tính nhanh
a.(1+1/2)×(1+1/3)×(1+1/4)×...×(1+1/98)×(1+1/99).
b.1/2×2/3×3/4×...×97/98×98/99×99/100
a,=3/2*4/3*....100/99
=3*4*5*....*100/2*3*...*99
=100/2=50
b, nhân lên băng:
1*2*3*...*99/2*3*...*100=1/100
cho T = 1/2 + 1/3 + 1/4 +....+ 1/99 + 1/100 và M = 1/99 + 2/98 + 3/97 + ...+ 97/3 + 98/2 +99/1
hãy tìm tỉ số T/M
\(\frac{T}{M}=\frac{\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+...+\frac{1}{100}}{\frac{1}{99}+\frac{2}{98}+...+\frac{98}{2}+\frac{99}{1}}\)
Xét M - 99 + 98 = \(\frac{100}{99}+\frac{100}{98}+...+\frac{100}{2}\)
\(\Leftrightarrow M-1=100\left(\frac{1}{2}+\frac{1}{3}+...+\frac{1}{99}\right)\)
\(\Rightarrow M=\frac{100}{100}+100\left(\frac{1}{2}+\frac{1}{3}+...+\frac{1}{99}\right)=100\left(\frac{1}{2}+\frac{1}{3}+...+\frac{1}{100}\right)\)
\(\Rightarrow\frac{T}{M}=\frac{\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+...+\frac{1}{100}}{100\left(\frac{1}{2}+\frac{1}{3}+...+\frac{1}{100}\right)}=\frac{1}{100}\)
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