tính nhanh : 1 + [1 +2 ] + [1 +2 +3 ] + [1 + 2 +3 +4 ] + .... + [1 + 2 +3 +4 +.....+100 ]
Những câu hỏi liên quan
tính nhanh (2/3+3/4+5/6+...+99/100).(1/2+2/3+3/4+...+98/99)-(1/2+1/3+...+99/100).(2/3+2/4+...+98/99)
1)Tính nhanh: A=1+3+3^2+3^3+3^4+...+3^100
B= 1+4^2+4^4+4^6+...+4^100
2) Cho biết 1^2+2^3+3^2+4^2+...+10^2= 385
Tính a) S1= 2^2+4^2+...+20^2
. b) S2= 100^2+200^2+...1000^2
Bài 1:
A = 1 + 3 + 32 + ... + 3100
=> 3A = 3 + 32 + ... + 3101
=> 2A = 3101 - 1
=> A = \(\frac{3^{101}-1}{2}\)
B = 1 + 42 + 44 + ... + 4100
=> 8B = 42 + 44 + ... + 4102
=> 7B = 4102 - 1
=> B = \(\frac{4^{102}-1}{7}\)
Bài 2:
a) S1 = 22 + 42 + ... + 202
=> S1 = 22(1+22+...+102)
=> S1 = 22.385
=> S1 = 1540
b) S2 = 1002 + 2002 + ... + 10002
=> S2 = 1002(1+22+...+102)
=> S2 = 1002.385
=> S2 = 3850000
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5 tháng 2 2022 lúc 15:48
tính nhanh (1+2+3+...+99+100).(1/2-1/3-1/7-1/9)(63.1,2-21.3,6)/1-2+3-4+...+99-100
Ta có \(63,1.2-21,3.6=0,9.7.10.1,2-21.3,6\)
\(=6,3.1,2-21.3,6\)
\(=0,9.7.4.3-7.3.0,9.4\)
\(=6,3.1,2-6,3.1,2\)
\(=0\)
\(\Rightarrow\dfrac{\left(1+2+......+100\right).\left(\dfrac{1}{2}-\dfrac{1}{3}-\dfrac{1}{7}-\dfrac{1}{9}\right)\left(63.1,2-21.3,6\right)}{1-2+3-4+.....+99-100}=\dfrac{\left(1+2+.....+100\right)\left(\dfrac{1}{2}-\dfrac{1}{3}-\dfrac{1}{7}-\dfrac{1}{9}\right)0}{1-2+3-4+......+99-100}=0\)
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Tính nhanh
a) 1 + 2 + 3 + … + 99 + 100 b) 2 + 4 + 6 + … + 96 + 98
c) (–1) + 2 + (–3) + 4 + … + (–99) +100 d) –1 + 2 – 3 + 4 – … – 99 + 100
Tính nhanh:
A=3/1+3/1+2+3/1+2+3+3/1+2+3+4+...+3/1+2+3+...+100
Nhanh hộ mình nhé
\(\frac{3}{1}+\frac{3}{1+2}+\frac{3}{1+2+3}+...+\frac{3}{1+2+...+100}\)
\(=3\left(\frac{1}{\frac{1\cdot2}{2}}+\frac{1}{\frac{2\cdot3}{2}}+\frac{1}{\frac{3\cdot4}{2}}+...+\frac{1}{\frac{100\cdot101}{2}}\right)\)
\(=3\left(\frac{2}{1\cdot2}+\frac{2}{2\cdot3}+...+\frac{2}{100\cdot101}\right)\)
\(=6\left(\frac{1}{1\cdot2}+\frac{1}{2\cdot3}+...+\frac{1}{100\cdot101}\right)\)
\(=6\left(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{100}-\frac{1}{101}\right)\)
\(=6\left(1-\frac{1}{101}\right)=6-\frac{6}{101}=\frac{606-6}{101}=\frac{600}{101}\)
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1+1+2+2+3+3+4+4+5+5+.........+100+100
Tính nhanh
1. tính nhanh
3/ 1 + 3/1+2 + 3/1+2+3 + 3/1+2+3+4 + ... + 3/1+2+3+4+...+100
3/1 + 3/1+2 + 3/1+2+3 + 3/1+2+3+4 + ... + 3/1+2+3+4+...+100
= 3 × (1/0+1 + 1/1+2 + 1/1+2+3 + 1/1+2+3+4 + ... + 1/1+2+3+4+...+100)
= 3 × (1/(1+0)×2:2 + 1/(1+2)×2:2 + 1/(1+3)×3:2 + 1/(1+4)×4:2 + ... + 1/(1+100)×100:2)
= 3 × (2/1×2 + 2/2×3 + 2/3×4 + 2/4×5 + ... + 2/100×101)
= 3 × 2 × (1/1×2 + 1/2×3 + 1/3×4 + 1/4×5 + ... + 1/100×101)
= 6 × (1 - 1/2 + 1/2 - 1/3 + 1/3 - 1/4 + 1/4 - 1/5 + ... + 1/100 - 1/101)
= 6 × (1 - 1/100)
= 6 × 100/101
= 600/101
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3/1 + 3/1+2 + 3/1+2+3 + ..................... + 3/1+2+3+4+ ...+100
= 3 x [1/1 + 1/1x3 +1/2x3 +1/2x5 +1/3x5 +1/3x7 + ... 1/50 x 99 +1/50 x 101]
= 3 x [1/1 x (1/1+1/3) +1/2 x (1/3+1/5) + 1/3 x(1/5+1/7) + ... + 1/50 x (1/99+1/101)
= 3 x (4/1x3 +4/3x5 +4/5x7 + ... 4/99x101)
= 3 x [(4/1 -4/3 +4/3 -4/5 +4/5 -4/7+...4/99 -4/101) : 2]
= 3 x [(4/1-4/101) :2]
= 3 x 200/101
= 600/101
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tính nhanh:(2+4+6+...+100)x[3/5:0,7+3x(-2/7)]:(1/2+1/4+1/6+...+1/100)
\(\left(2+4+6+...+100\right).\left[\frac{3}{5}:0,7+3.\frac{-2}{7}\right]:\left(\frac{1}{2}+\frac{1}{4}+...+\frac{1}{100}\right)\)
Để í ngoặc \(\left[\frac{3}{5}:0,7+3.\frac{-2}{7}\right]\)
\(\Leftrightarrow\left[\frac{6}{7}+-\frac{6}{7}\right]\)
\(\Leftrightarrow0\)
Vậy biểu thức \(\left(2+4+6+...+100\right).\left[\frac{3}{5}:0,7+3.\frac{-2}{7}\right]:\left(\frac{1}{2}+\frac{1}{4}+...+\frac{1}{100}\right)\)có giá trị bằng 0
Mn ơi giải giúp mình bài này với ạ. Mình đang cần gấp
Tính tổng
1/1+1^2+1^4 + 2/1+2^2+2^4 + 3/1+3^2+3^4 +.......+ 100/1+100^2+100^4
Thx nha ai nhanh thì mình tick dấu cho nha