1+1+2+2+3+3=
Chứng minh rằng:
a,A=1/2+1/2^2+1/2^3+.+1/2^2<1
b,B=1/3+1/3^2+1/3^3+...+1/3^n<1/2
c,B=1/2-1/2^2+1/2^3-1/2^4+...+1/2^2015-1/2^2016<1/3
d,D=1/3+2/3^2+3/3^3+4/3^4+...+100/3^100<3/4
?reeeeeeeeeeee
Ủa, cái số gì đây??????
Tính:
2 - 1 = 3 - 1 = 1 + 1 = 1 + 2 =
3- 1 = 3 - 2 = 2 - 1 = 3 - 2 =
3 -2 = 2 - 1 = 3 - 1 = 3 - 1 =
2 - 1 = 1 3 - 1 = 2 1 + 1 = 2 1 + 2 = 3
3 - 1 = 2 3 - 2 = 1 2 - 1 = 1 3 - 2 = 1
3 - 2 = 1 2 - 1 = 1 3 - 1 = 2 3 - 1 = 2
2 - 1 = 1 3 - 1 = 2 1 + 1 = 2 1 + 2 = 3
3 - 1 = 2 3 - 2 = 1 2 - 1 = 1 3 - 2 = 1
3 - 2 = 1 2 - 1 = 1 3 - 1 = 2 3 - 1 = 2
ok nhá
Tính:
| 1 + 2 = … | 3 – 1 = … | 1 + 1 = … | 2 – 1 = … |
| 3 – 2 = … | 3 – 2 = … | 2 – 1 = … | 3 – 1 = … |
| 3 – 1 = … | 2 – 1 = … | 3 – 1 = … | 3 – 2 = … |
Lời giải chi tiết:
| 1 + 2 = 3 | 3 – 1 = 2 | 1 + 1 = 2 | 2 – 1 = 1 |
| 3 – 2 = 1 | 3 – 2 = 1 | 2 – 1 = 1 | 3 – 1 = 2 |
| 3 – 1 = 2 | 2 – 1 = 1 | 3 – 1 = 2 | 3 – 2 = 1 |
| 1+2=3 | 3-1=2 | 1+1=2 | 2-1=1 |
| 3-2=1 | 3-2=1 | 2-1=1 | 3-1=2 |
| 3-1=2 | 2-1=1 | 3-1=2 | 3-2=1 |
#HT#
1. 3, 2, 2, 1.
2. 1 ,1 ,1 ,2.
3. 2, 1, 2, 1.
HT!
Tính nhanh
1+2+3+1+2+3+1+2+3+1+2+3+1+2+3+1+2+3+1+3+2+1+2+3+1+2+3=
Đọc kĩ đề
1+2+3+1+2+3+1+2+3+1+2+3+1+2+3+1+2+3+1+2+3+1+2+3+1+2+3
= 6+6+6+6+6+6+6+6+6
= 6x9
= 54
Tính giá trị biểu thức
a, A = (1 - 1/1+2) . (1 - 1/1+2+3) . (1- 1/1+2+3+4) . ... .(1- 1/1+2+...+100)
b, B = (2/3+ 3/4 +...+99/100).(1/2+2/3+...+98/99) - (1/2+2/3+...+99/100).(2/3+3/4+...+98/99)
c, C = \(\frac{3^3+1^3}{2^3-1^3}+\frac{5^3+2^3}{3^3-2^3}+\frac{7^3+3^3}{4^3-3^3}+...+\frac{41^3+20^3}{21^3-20^3}\)
ềdfđừytretwrerfwrevcreerwaruircewtdyererrrrrrrrrrrrrrrrdbrbr trưewyt ưt rtf gygr frirfy gfyrgfyur uỷ gyurg rfuy frg egfyryfyrty trg r rei eoer7 87re r7ye7i t 87rt 7 t ryigr yyrggfygfhdg gfhg gf fgg jdfgjh f fggfgfg jffg jfg f gfg fjhg hjfg gfsdj fgdj gfdjfgdjhf gjhg f gfg fk f fjk hjkfghjkfg h hjyjj ỵthj
bài 1:
1/4 + 2/3 2/7 + 2/3 2/5 + 1/3 2/3 + 1/2 1/3 + 3/5 4/5 + 1/3
1/8 + 3/4 1/36 + 5/12 1/3 + 1/6 + 1/18.
bài 2:
15/16 - 3/16 17/18 - 5/6 3/4 - 4/9 1/2 - 2/5 5/6 - 3/10 3-1/3
4/5 - 1/10 5/2 - 1 5/8 - 2/5.
Bài 1:
\(\frac14+\frac23=\frac{3}{12}+\frac{8}{12}=\frac{3+8}{12}=\frac{11}{12}\)
\(\frac27+\frac23=\frac{6}{21}+\frac{14}{21}=\frac{6+14}{21}=\frac{20}{21}\)
\(\frac25+\frac13=\frac{6}{15}+\frac{5}{15}=\frac{6+5}{15}=\frac{11}{15}\)
\(\frac23+\frac12=\frac46+\frac36=\frac{4+3}{6}=\frac76\)
\(\frac13+\frac35=\frac{5}{15}+\frac{9}{15}=\frac{5+9}{15}=\frac{14}{15}\)
\(\frac45+\frac13=\frac{12}{15}+\frac{5}{15}=\frac{12+5}{15}=\frac{17}{15}\)
\(\frac18+\frac34=\frac18+\frac68=\frac{1+6}{8}=\frac78\)
\(\frac{1}{36}+\frac{5}{12}=\frac{1}{36}+\frac{15}{36}=\frac{1+15}{36}=\frac{16}{36}=\frac49\)
\(\frac13+\frac16+\frac{1}{18}=\frac{6}{18}+\frac{3}{18}+\frac{1}{18}=\frac{6+3+1}{18}=\frac{10}{18}=\frac59\)
Bài 2:
\(\frac{15}{16}-\frac{3}{16}=\frac{15-3}{16}=\frac{12}{16}=\frac34\)
\(\frac{17}{18}-\frac56=\frac{17}{18}-\frac{15}{18}=\frac{17-15}{18}=\frac{2}{18}=\frac19\)
\(\frac34-\frac49=\frac{27}{36}-\frac{16}{36}=\frac{27-16}{36}=\frac{11}{36}\)
\(\frac12-\frac25=\frac{5}{10}-\frac{4}{10}=\frac{5-4}{10}=\frac{1}{10}\)
\(\frac56-\frac{3}{10}=\frac{25}{30}-\frac{9}{30}=\frac{25-9}{30}=\frac{16}{30}=\frac{8}{15}\)
\(3-\frac13=\frac93-\frac13=\frac{9-1}{3}=\frac83\)
\(\frac45-\frac{1}{10}=\frac{8}{10}-\frac{1}{10}=\frac{7}{10}\)
\(\frac52-1=\frac{5-2}{2}=\frac32\)
\(\frac58-\frac25=\frac{25}{40}-\frac{16}{40}=\frac{25-16}{40}=\frac{9}{40}\)
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)
a: Ta có công thức tổng quát:
\(1-\frac{1}{1+2+\cdots+n}\)
\(=1-\frac{1}{\frac{n\left(n+1\right)}{2}}=1-\frac{2}{n\left(n+1\right)}\)
\(=\frac{n\left(n+1\right)-2}{n\left(n+1\right)}=\frac{n^2+n-2}{n\left(n+1\right)}=\frac{\left(n+2\right)\left(n-1\right)}{n\left(n+1\right)}\)
Ta có: \(A=\left(1-\frac{1}{1+2}\right)\left(1-\frac{1}{1+2+3}\right)\cdot\ldots\cdot\left(1-\frac{1}{1+2+\cdots+2022}\right)\)
\(=\frac{\left(2+2\right)\left(2-1\right)}{2\left(2+1\right)}\cdot\frac{\left(3+2\right)\left(3-1\right)}{3\left(3+1\right)}\cdot\ldots\cdot\frac{\left(2022+2\right)\left(2022-1\right)}{2022\left(2022+1\right)}\)
\(=\frac{4\cdot5\cdot\ldots\cdot2024}{3\cdot4\cdot\ldots\cdot2023}\cdot\frac{1\cdot2\cdot\ldots\cdot2021}{2\cdot3\cdot\ldots\cdot2022}=\frac{2024}{3}\cdot\frac{1}{2022}=\frac{1012}{1011\cdot3}=\frac{1012}{3033}\)
b:Sửa đề: \(B=1+\frac12\left(1+2\right)+\frac13\left(1+2+3\right)+\cdots+\frac{1}{100}\left(1+2+\cdots+100\right)\)
\(=1+\frac12\cdot\frac{2\cdot3}{2}+\frac13\cdot\frac{3\cdot4}{2}+\cdots+\frac{1}{100}\cdot\frac{100\cdot101}{2}\)
\(=1+\frac32+\frac42+\cdots+\frac{101}{2}=\frac12\left(2+3+4+\cdots+101\right)\)
\(=\frac12\left(101-2+1\right)\cdot\frac{101+2}{2}=\frac12\cdot100\cdot\frac{101+2}{2}=103\cdot25=2575\)
Điền vào ô vuông các dấu thích hợp (=, <,>)
1^2 ... 1
2^2 ... 1+3
3^2 ...1+3+5
1^3 ... 1^2 - 0^2
2^3 ... 3^2 - 1^2
3^3 ... 6^2 - 3^2
4^3 ... 10^2 - 6^2
(0+1)^2 ... 0^2 + 1^2
(1+2)^2 ... 1^2 + 2^2
(2 + 3)^2 ... 2^3 + 3^2
Lời giải chi tiết
12
1 13
12 – 02 (0 + 1)2
02 +12
22
1 + 3 23
32 – 12 (1 + 2)2
12 + 22
32
1 + 3 + 5 33
62 – 32 (2 + 3)2
22 + 32
43
102 – 62
= , = , = , = , = , > nhé
GHGH3UG TRGGHJg ytg gjgdgfgh ẻughrkhfkjrthgh] ơyt]ơ ươ]y[ươ] ơ]m ơ]ơ] ơu]y[ ưu[y ưuy[ ưu[y] y[ợ]uợ]uợ]uợu]j[u]j[u]j[u]j[u]j[u]j[u]ơu]j[ựu[ụ]uợ]uơ]uợu] uhyiuu5yturyytytyytyytty8ytytytytyty58yt85yt85y8ty85yt85y8ty58yt85yt85yt85y8t5yt8y58ty58yt85yt85yt85y58tyyyr5ybtyurygytbgbrbvtterytiburbyvfudytubertuygtdrtuufutydiytuiydyiuyuityurdyiutyruytiurdyuitiurtuyrdytuiyryritrybtiyryrtiutybbirybtreybruiiurytryvui
Các phân số 1/3: 1/6: 5/2: 3/2 xếp theo thứ tự tăng dần
a. 1/3; 1/6; 5/2; 3/2 b. 1/3; 5/2; 1/6; 3/2 c. 1/6; 1/3; 3/2; 5/2 d. 1/6; 3/2; 3/2; 5/2
Chứng minh rằng:
a) A=1/2^2+1/3^2+1/4^2+...+1/2010^2<1
b) B=1/2+2/2^2+3/2^3+...+100/2^100<2
c) C=1/3+2/3^2+3/3^3+...+100/3^100<3/4
d) D=1/2^3+1/3^3+1/4^3+...+1/n^3<1/4 (n€ N;n> hoặc = 3)
e) E=1/3^3+1/4^3+1/5^3+...+1/n^3<1/12 (n€N; n> hoặc = 3)
f) F=2/1*4/3*6/5*...*200/199<20
g) G=3/4+5/36+7/144+...+2n+1/n^2*(n+1)^2<1 (n nguyên dương)
h) H=1/2*(1/6+1/24+1/60+...+1/9240)>57/462
i) I=1/31+1/32+1/33+...+1/2048>3
j) J=(1-1/3)*(1-1/6)*(1-1/10)*...*(1-1/253)<2/5
k) K=1/2!+2/3!+3/4!+...+n-1/n! (n€N;n> hoặc = 2)
l) L=1/2!+5/3!+11/4!+...+n^2+n-1/(n+1)!<2
m) 1/6M=1/5^2+1/6^2+1/7^2+...+1/100^2<1/4
Có thể mình hơi phũ tí nhưng mình bảo đảm một thế kỉ sau sẽ không ai ngồi giải hết đống bài này cho bạn đâu, hỏi từng câu thôi
P/s: chắc bạn đánh mỏi tay lắm
Ta có: D<1/1.2.3+1/2.3.4+1/3.4.5+...+1/(n-1).n.(n+1)
D<1/2.(2/1.2.3+2/2.3.4+2/3.4.5+...+2/(n-1).n.(n+1))
D<1/2.(1/1.2-1/2.3+1/2.3-1/3.4+1/3.4-1/4.5+...+1/(n-1).n-1/n.(n+1))
D<1/2.((1/2-1/n.(n+1))
D<1/4-1/2.n.(n+1)<1/4
D<1/4