A=(1+1/2) (1+1/3) (1+1/4)...(1+1/100)
H24
Những câu hỏi liên quan
a ) A = 1/4 + 1/4^2 +1/4^3 +.........+ 1/4^100 + 1/3.4^100
b) B = 1/3 - 1/3^2 + 1/3^3 - 1/3^4 +.........+ 1/ 3^99
a)Ta có :
\(A=\dfrac{1}{4}+\dfrac{1}{4^2}+\dfrac{1}{4^3}+............+\dfrac{1}{4^{100}}\)
\(4A=1+\dfrac{1}{4}+\dfrac{1}{4^2}+\dfrac{1}{4^3}+..........+\dfrac{1}{4^{99}}\)
\(4A-A=\left(1+\dfrac{1}{4}+.......+\dfrac{1}{4^{99}}\right)-\left(\dfrac{1}{4}+\dfrac{1}{4^2}+.....+\dfrac{1}{4^{100}}\right)\)
\(3A=1-\dfrac{1}{4^{100}}\)
\(\Rightarrow A=\dfrac{1-\dfrac{1}{4^{100}}}{3}\)
~ Chúc bn học tốt ~
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CMR:
a)1/10^2 +1/11^2+1/12^2+...+1/100^2 >3/4
b)1/2^2+1/3^2+1/4^2+...+1/100^2<99/100
c)1/2^2+1/3^2+1/4^2+...+1/100^2<3/4
Tính:
A=(1-1/1+2).(1-1/1+2+3).(1-1/1+2+3+4)...(1-1/1+2+3+4+...+2022)
B=1+1/2(1+2)+1/3(1+2+3)+1/100(1+2+3+...+100)
Bài 4 :
a,Cho A= 1/2!+1/3!+.....+1/100!
CMR A<1
b, CMR :1-1/2+1/3-1/4+...+1/99-1/100=1/51+1/52+....+1/100
Chứng minh rằng :
a,1- 1/2 + 1/3 - 1/4 + 1/5 - 1/6 + ...... + 1/ 99 - 1/ 100 = 1 / 51 + 1/ 52 + 1/ 53 + ... + 1/ 100
b, A= 1/3 - 2/ 32 + 3/ 33 - 4/ 34 + .... + 99/ 399 - 100/ 3100 < 3/ 16
\(1-\frac{1}{2}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{99}-\frac{1}{100}=\left(1+\frac{1}{3}+\frac{1}{5}+...+\frac{1}{99}\right)-\left(\frac{1}{2}+\frac{1}{4}+...+\frac{1}{100}\right)\)
\(=\left(1+\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+...+\frac{1}{99}+\frac{1}{100}\right)-2\left(\frac{1}{2}+\frac{1}{4}+\frac{1}{6}+...+\frac{1}{100}\right)\)
\(=\left(1+\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+...+\frac{1}{100}\right)-\left(1+\frac{1}{2}+\frac{1}{3}+...+\frac{1}{50}\right)=\frac{1}{51}+\frac{1}{52}+...+\frac{1}{100}\)
\(\RightarrowĐPCM\)
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Xem thêm câu trả lời
Tính
a) (x-1/2)+(x-1/4)+(x-1/8)+...+(x-1/512)
Tìm x
a) (x-1/1×2)+(x-1/2×3)+...+(x-1/100×101)
b) (x-1)+(x-2)+(x-3)+...+(x-101)=5050
c) x+1/2+1/3+1/4+...+1/100=3/2+4/3+5/4++...+101/100
Chứng minh rằng :
a,1- 1/2 + 1/3 - 1/4 + 1/5 - 1/6 + ...... + 1/ 99 - 1/ 100 = 1 / 51 + 1/ 52 + 1/ 53 + ... + 1/ 100
b, A= 1/3 - 2/ 32 + 3/ 33 - 4/ 34 + .... + 99/ 399 - 100/ 3100 < 3/ 16
Giup tui nha ... Lam on ma
a,(1-1/2)*(1-1/3)*(1-1/4)....(1-1/99)*(1-1/100)
b,(1+1/2)*(1+1/3)*(1+1/4)....(1+1/99)*(1+1/100)
a) \(\left(1-\frac{1}{2}\right)\cdot\left(1-\frac{1}{3}\right)\cdot\left(1-\frac{1}{4}\right)\cdot...\cdot\left(1-\frac{1}{99}\right)\cdot\left(1-\frac{1}{100}\right)\)
\(=\frac{1}{2}\cdot\frac{2}{3}\cdot\frac{3}{4}\cdot...\cdot\frac{98}{99}\cdot\frac{99}{100}\)
\(=\frac{1\cdot2\cdot3\cdot...\cdot98\cdot99}{2\cdot3\cdot4\cdot...\cdot99\cdot100}=\frac{1}{100}\)
b) \(\left(1+\frac{1}{2}\right)\cdot\left(1+\frac{1}{3}\right)\cdot\left(1+\frac{1}{4}\right)\cdot...\cdot\left(1+\frac{1}{99}\right)\cdot\left(1+\frac{1}{100}\right)\)
\(=\frac{3}{2}\cdot\frac{4}{3}\cdot\frac{5}{4}\cdot...\cdot\frac{100}{99}\cdot\frac{101}{100}\)
\(=\frac{3\cdot4\cdot5\cdot...\cdot100\cdot101}{2\cdot3\cdot4\cdot...\cdot99\cdot100}=\frac{101}{2}\)
Tính:
A=1*2*3+2*3*4+3*4*5+......+98*99*100
CMR:
A=1/4+1/16+1/36+1/64+1/100+1/144+1/196<1/2
A=\(\frac{1}{4}+\frac{1}{16}+\frac{1}{36}+\frac{1}{64}+\frac{1}{100}+\frac{1}{144}+\frac{1}{196}\)=\(\frac{1}{2^2}+\frac{1}{4^2}+\frac{1}{6^2}+\frac{1}{8^2}+\frac{1}{10^2}+\frac{1}{12^2}+\frac{1}{14^2}\)
=>A<\(\frac{1}{2.2}+\frac{1}{2.4}+\frac{1}{4.6}+\frac{1}{6.8}+\frac{1}{8.10}+\frac{1}{10.12}+\frac{1}{12.14}\)
=>A<\(\left(\frac{1}{2}-\frac{1}{2}+\frac{1}{2}-\frac{1}{4}+\frac{1}{4}-\frac{1}{6}+...+\frac{1}{12}-\frac{1}{14}\right)\)\(:2\)=\(\left(\frac{1}{2}-\frac{1}{14}\right):2\)<\(\frac{1}{2}\)
=>A<\(\frac{1}{2}\)
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1. Chứng tỏ rằng tổng 100 số đầu tiên của dãy sau nhỏ hơn 1/4:1/5; 1/45;1/117;1/221;1/357;...2.tính A/B biết:A1/1.300+1/2.301+1/3.302+...+1/101.400B1/1.102+1/2.103+...+1/299.4003.Chứng minh rằng; 100-(1+1/2+1/3+...+1/100)1/2+2/3+...+99/1004. Tính A/B biết : A1/2+1/3+...+1/200B1/199+2/198+...+199/15. Tính: 1-1/2+1/3-1/4+...+1/99-1/100 phần 1/51+1/52+...+1/100giúp mk nha, ai nhanh mk k cho!
Đọc tiếp
1. Chứng tỏ rằng tổng 100 số đầu tiên của dãy sau nhỏ hơn 1/4:
1/5; 1/45;1/117;1/221;1/357;...
2.tính A/B biết:
A=1/1.300+1/2.301+1/3.302+...+1/101.400
B=1/1.102+1/2.103+...+1/299.400
3.
Chứng minh rằng; 100-(1+1/2+1/3+...+1/100)=1/2+2/3+...+99/100
4. Tính A/B biết : A=1/2+1/3+...+1/200
B=1/199+2/198+...+199/1
5. Tính: 1-1/2+1/3-1/4+...+1/99-1/100 phần 1/51+1/52+...+1/100
giúp mk nha, ai nhanh mk k cho!