1x1= 6x6=
2x2= 7x7=
3x3= 8x8=
4x4= 9x9=
5x5= 10x10=
1x1=
2x2=
3x3=
4x4=
5x5=
6x6=
7x7=
8x8=
9x9=
10x10=
1 x 1 = 1
2 x 2 = 4
3 x 3 = 9
4 x 4 = 16
5 x 5 = 25
6 x 6 = 36
7 x 7 = 49
8 x 8 = 64
9 x 9 = 81
10 x 10 = 100
\(1x1=1\)
\(2x2=4\)
\(3x3=9\)
\(4x4=16\)
\(5x5=25\)
\(6x6=36\)
\(7x7=49\)
\(8x8=64\)
\(9x9=81\)
\(10x10=100\)
1 x 1 = 1
2 x 2 = 4
3 x 3 = 9
4 x 4 = 16
5 x 5 = 25
6 x 6 = 36
7 x 7 = 49
8 x 8 = 64
9 x 9 = 81
10 x 10 = 100
Tổng: 1 + 2x2 + 3x3 + 4x4 + 5x5 + 6x6 + 7x7 + 8x8 + 9x9 + 10x10 là bao nhiêu?
1 + 2 x 2 + 3 x 3 + 4 x 4 + 5 x 5 + 6 x 6 + 7 x 7 + 8 x 8 + 9 x 9 + 10 x 10
= 1 + 4 + 9 + 16 + 25 + 36 + 49 + 64 + 81 + 100
= 385
1 + 2x2 + 3x3 + 4x4 + 5x5 + 6x6 + 7x7 + 8x8 + 9x9 + 10x10
= 1+4+9+16+25+36+49+64+81+100
=(81+9)+(64+16)+(49+1)+)36+4)+25+100
=90+80+50+40+25 +100
=385
1x1=
2x2=
3x3=
4x4=
5x5=
6x6=
7x7=
8x8=
9x9=
10x10=
11x11=
12x12=
13x13=
14x14=
15x15=
16x16=
17x17=
18x18=
19x19=
20x20=
ai đúng mình tích
1x1=1
2x2=4
3x3=9
4x4=16
5x5=25
6x6=36
7x7=49
8x8=64
9x9=81
10x10=100
11x11=121
12x12=144
13x13=169
14x14=196
15x15=225
16x16=256
17x17=289
18x18=324
19x19=361
20x20=400
Tính bằng cách thuận tiện nhất:
1/2x2/3x3/4x4/5x5/6x6/7x7/8x8/9
So sánh số sau: 1/2x2+1/3x3+1/4x4+1/5x5+1/6x6+1/7x7+1/8x8 với 1.
đặt \(A=\frac{1}{2.2}+\frac{1}{3.3}+\frac{1}{4.4}+\frac{1}{5.5}+\frac{1}{6.6}+\frac{1}{7.7}+\frac{1}{8.8}=\frac{1}{2^2}+\frac{1}{3^2}+\frac{1}{4^2}+\frac{1}{5^2}+\frac{1}{6^2}+\frac{1}{7^2}+\frac{1}{8^2}\)
\(A
Chứng tỏ rằng
B=\(\frac{1}{2x2}+\frac{1}{3x3}+\frac{1}{4x4}+\frac{1}{5x5}+\frac{1}{6x6}+\frac{1}{7x7}+\frac{1}{8x8}< 1\)
Ta thấy:
1/2*2<1/1*2)vì 2*2>1*2).
1/3*3<1/2*3(vì 3*3>2*3).
...
1/8*8<1/7*8(vì 8*8>7*8).
=>1/2*2+1/3*3+1/4*4+...+1/8*8<1/1*2+1/2*3+1/3*4+...+1/7*8.
=>B<1-1/2+1/2-1/3+1/3-1/4+1/4-1/5+1/5-1/6+1/6-1/7+1/7-1/8.
=>B<1-1/8.
=>B<7/8.
Mà 7/8<1.
=>B<1.
Vậy B<1(đpcm).
\(< \frac{1}{1\cdot2}+\frac{1}{2\cdot3}+\frac{1}{3\cdot4}+\frac{1}{4\cdot5}+\frac{1}{5\cdot6}+\frac{1}{6\cdot7}+\frac{1}{7\cdot8}\)
\(\Rightarrow1-\frac{1}{8}< 1\)
=>B<1
\(B=\frac{1}{2.2}+\frac{1}{3.3}+\frac{1}{4.4}+\frac{1}{5.5}+\frac{1}{6.6.}+\frac{1}{7.7}+\frac{1}{8.8}\)\(=\)\(\frac{1}{2^2}+\frac{1}{3^2}+\frac{1}{4^2}+\frac{1}{5^2}+\frac{1}{6^2}+\frac{1}{7^2}+\frac{1}{8^2}\)
\(B=\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+\frac{1}{5.6}+\frac{1}{6.7}+\frac{1}{7.8}\)
\(B=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+...+\frac{1}{7}-\frac{1}{8}\)
\(B=1-\frac{1}{8}\)
\(\Rightarrow B< 1\left(ĐPCM\right)\)
cho mình hỏi là bài tính nhanh 1/2x2/3x3/4x4/5x5/6x6/7x7/8 làm như thế nào ạ
A=1x2+2x3+3x4+...+49x50
B=1x3+3x5+5x7+...+99x101
C=1x2x3+2x3x4+3x4x5+...+50x51x52
D=1x4+2x5+3x6+...+60x63
E=1x1+2x2+3x3+...+50x50
F=1x1+3x3+5x5+...+71x71
G=1x1+4x4+7x7+...+100x100
I=1x2x3+3x4x5+5x6x7+...+69x70x71
A=1x2+2x3+3x4+...+49x50
3A= 3(1.2+2.3+3.4+...+49.50)
3A= 1.2.3+2.3.3+3.4.3+...+49.50.3
3A= 1.2.(3-0)+2.3(4-1)+3.4(5-2)+...+49.50.(51-48)
3A= 0.1.2-1.2.3+1.2.3-2.3.4+2.3.4-3.4.5+...+48.49.50-49.50.51
3A= 49.50.51
A= 49.50.51/3=41650
B=1x3+3x5+5x7+...+99x101
B=1/1.3 +1/3.5 +...+1/99.101
2B=2/1.3 + 2/3.5 +...+2/99.101
2B=1-1/3+1/3-1/5+...+1/99-1/101
2B=1-1/101
2B=100/101
B=100/101:2=100/202
C=1x2x3+2x3x4+3x4x5+...+50x51x52
Nhân C với 4 ta được:
C x 4 = 1x2x3x4 + 2x3x4x 4 + 3x4x5x4 +…+50x51x52x4
C x 4 = 1x2x3x4 + 2x3x4x(5-1) + 3x4x5x(6-2) + ... + 50x51x52x(53-49)
C x 4 = 1x2x3x4 + 2x3x4x5 - 1x2x3x4 + 3x4x5x6 - 2x3x4x5 + ... +49x 50x51x52 - 50x51x52x53
Sau khi cộng - trừ giản ước ta có : C x 4 = 50x51x52x53
C = 50x51x52x53 : 4 = 1756950
E=1x1+3x3+5x5+7x7+...+25x25
F=4x4+7x7+10x10+...+19x19
giúp mik với thank các bn
E= 2925
F= 951
nho k cho minh nha minh dang can diem
E= 1x1+3x3+5x5+7x7+9x9+11x11+13x13+15x15+17x17+19x19+21x21+25x25=2925
F= 4x4+7x7+10x10+13x13+16x16+19x19=951
bai nhu vay day cho minh xin mot k nha ko co cung duoc