3(5+42+43+...+449) =43x-1-1
Những câu hỏi liên quan
hãy chứng tỏ rằng : 1/41 + 1/42 + 1/43 + ... + 1/80 > 3/5
CM: 41/2×42/2×43/2×.....×80/2=1×3×5×....×79
bài 1:Tính nhanh
a,64*25+35*25+25
b,58*42+32*8+5*16
c,(42*43+43*57+43)-360/4
d,(372-19*4)+(981/9-13)
e,456/2*8+456/3-102
a)2500
b)2772
c)1974
d)347
e)1874
k mk nha
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Giải phương trình
7
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4
3
x
-
4
2
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3
x
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4
0
A.
x
-
log
2
+
3...
Đọc tiếp
Giải phương trình 7 + 4 3 x - 4 2 + 3 x + 4 = 0
A. x = - log 2 + 3 2
B. x = log 2 + 3 2
C. x = - log 2 + 3 4
D. x = log 2 + 3 4
Thực hiện các phép tính sau :
1, 37 - 58 + 75 - 58
2, 49 - 54 + 41 - 52 + 59
3, 43 - 27 - 43 - 38 + 27
4, 18 - 43 - ( 18 - 43 ) - 51
5, ( 37 - 54 - 43 ) - ( 37 - 54 + 42 )
6, - ( 39 - 42 + 38 ) - ( 42 - 39 +38 ) + 95
Ai trả lời nhanh mình k cho !!!!! ^-^
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Chứng tỏ 1/41+1/42+1/43+...1/80<5/8
a) S=1+2+22+23+...+22022
b)S=3+32+33+...+32022
c)S=4+42+43+...+42022
d)S=5+52+53+...+52022
a) \(S=1+2+2^2+..+2^{2022}\)
\(2S=2+2^2+2^3+...+2^{2023}\)
\(2S-S=2+2^2+2^3+...+2^{2023}-1-2-2^2-...-2^{2022}\)
\(S=2^{2023}-1\)
b) \(S=3+3^2+3^3+...+3^{2022}\)
\(3S=3^2+3^3+...+3^{2023}\)
\(3S-S=3^2+3^3+....+3^{2023}-3-3^2-...-3^{2022}\)
\(2S=3^{2023}-3\)
\(\Rightarrow S=\dfrac{3^{2023}-3}{2}\)
c) \(S=4+4^2+4^3+...+4^{2022}\)
\(4S=4^2+4^3+...+4^{2023}\)
\(4S-S=4^2+4^3+...+4^{2023}-4-4^2-...-4^{2022}\)
\(3S=4^{2023}-4\)
\(S=\dfrac{4^{2023}-4}{3}\)
d) \(S=5+5^2+...+5^{2022}\)
\(5S=5^2+5^3+...+5^{2023}\)
\(5S-S=5^2+5^3+...+5^{2023}-5-5^2-...-5^{2022}\)
\(4S=5^{2023}-5\)
\(S=\dfrac{5^{2023}-5}{4}\)
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Tính Nhanh:
1/2+5/6+11/12+19/20+29/30+41/42+42/43
\(\frac{1}{2}+\frac{5}{6}+\frac{11}{12}+\frac{19}{20}+\frac{29}{30}+\frac{41}{42}+\frac{42}{43}\)
\(=1-\frac{1}{2}+1-\frac{1}{6}+1-\frac{1}{12}+1-\frac{1}{20}+1-\frac{1}{30}+1-\frac{1}{42}+\frac{42}{43}\)
\(=6-\left(\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+\frac{1}{30}+\frac{1}{42}\right)+\frac{42}{43}\)
\(=6-\left(\frac{1}{1x2}+\frac{1}{2x3}+\frac{1}{3x4}+\frac{1}{4x5}+\frac{1}{5x6}\right)+\frac{42}{43}\)
\(=6-\left(1-\frac{1}{6}\right)+\frac{42}{43}\)
...
bn tự tính tiếp nha
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CMR : a) 1/41 + 1/42 + 1/43 +...+ 1/80 < 5/6
b) 1/2^2 + 1/2^4 + 1/2^6 +...+ 1/2^200 < 1/3