Tính H=\(\frac{1}{1x2}\) -\(\frac{1}{1x2x3}\) +\(\frac{1}{2x3}\) -\(\frac{1}{2x3x4}\) +\(\frac{1}{3x4}\) -\(\frac{1}{3x4x5}\) +...+\(\frac{1}{99x100}\) -\(\frac{1}{99x100x101}\)
tính nhanh
\(\frac{1}{1x2}+\frac{1}{2x3}+\frac{1}{3x4}+\frac{1}{4x5}+....+\frac{1}{99x100}\)
1/1×2 + 1/2×3 + 1/3×4 + 1/4×5 + ... + 1/99×100
= 1 - 1/2 + 1/2 - 1/3 + 1/3 - 1/4 + 1/4 - 1/5 + ... + 1/99 - 1/100
= 1 - 1/100
= 99/100
1. Tính tổng
\(\frac{1}{1x2x3}+\frac{1}{2x3x4}+\frac{1}{3x4x5}+.....+\frac{1}{18x19x20}\)
2. Tính nhanh
B = 1 x 1 + 2 x 2 + 3 x 3 + ......+ 100 x 100
3. Tính tổng
A = 4 + 16 + 36 + 64 +.....+ 10000
4. Tính tổng:
M = 1 + 9 + 25 + 49 + 9801
5. Tính nhanh:
\(\left(\frac{1}{51}+\frac{1}{52}+\frac{1}{53}+....+\frac{1}{100}\right):\left(\frac{1}{1x2}+\frac{1}{3x4}+\frac{1}{99x100}\right)\)
Nhớ cho mình cách giải nha. Ai làm nhanh, làm đúng sẽ được 10 tick
C=1x2+2x3+3x4+........+99x100
D=1x2x3+2x3x4+3x4x5+.......+98x99x100
E=12+22+52+.......+992
F=1/1x2+1/2x3+..........+1/99x100
G=1/1x2x3+1/2x3x4+........+1/99x98x100
H= 1/1x2x3x4+1/3x4x5x6+............+1/97x98x99x100
K= 1+1/2(1+2)+1/3(1+2+3)+........+1/30(1+2+30)
L=1/21+1/22+1/23+1/24+..............+1/210
M=2015/2015x2017-20162
\(\frac{ }{ }\)
sao nhiều vậy!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
F = 1- 1/2 + 1/2 - 1/3 + 1/3 - 1/4 + ... + 1/99 - 1/100
= 1 - 1/100
= 99/100
\(\frac{1}{1x2}+\frac{1}{2x3}+\frac{1}{3x4}+.....+\frac{1}{99x100}\)
\(A=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{99}-\frac{1}{100}\)
\(A=1-\frac{1}{100}=\frac{99}{100}\)
k cho mình nha bạn
=1-1/2+1/2-1/3+1/3-1/4+...+1/99-1/100
=1-1/100=99/100
\(\frac{1}{1x2x3}+\frac{1}{2x3x4}+\frac{1}{3x4x5}+...+\frac{1}{48x49x50}\)
\(\frac{1}{1.2.3}+\frac{1}{2.3.4}+......+\frac{1}{48.49.50}\)
\(=\frac{1}{2}.\left(\frac{1}{1.2}-\frac{1}{2.3}+\frac{1}{2.3}-\frac{1}{3.4}+....+\frac{1}{48.49}-\frac{1}{49.50}\right)\)
\(=\frac{1}{2}.\left(\frac{1}{1.2}-\frac{1}{49.50}\right)\)
\(=\frac{1}{2}.\frac{612}{1225}=\frac{612}{2450}=\frac{306}{1225}\)
Do not ask why hay quá!
Đặt \(T=\frac{1}{1.2.3}+\frac{1}{2.3.4}+\frac{1}{3.4.5}+...+\frac{1}{48.49.50}\)
Ta xét:
\(\frac{1}{1.2}-\frac{1}{2.3}=\frac{1}{1.2.3}\);\(\frac{1}{2.3}-\frac{1}{3.4}=\frac{1}{2.3.4}\);. . . ; \(\frac{1}{48.49}-\frac{1}{49.50}=\frac{1}{48.49.50}\)
Rút ra dạng tổng quát,ta có: (mình nói thêm nhé)
\(\frac{1}{n\left(n+1\right)}-\frac{1}{n\left(n+1\right)\left(n+2\right)}=\frac{1}{n\left(n+1\right)\left(n+2\right)}\)
\(\Rightarrow2T=\frac{1}{1.2}-\frac{1}{2.3}+\frac{1}{2.3}-\frac{1}{3.4}+...+\frac{1}{48.49}-\frac{1}{49.50}\)
Ta nhận thấy: \(-\frac{1}{2.3}+\frac{1}{2.3}=0\);\(-\frac{1}{3.4}+\frac{1}{3.4}=0\);.....
\(\Rightarrow2T=\frac{1}{1.2}-\frac{1}{49.50}=\frac{612}{1225}\)
\(\Rightarrow T=\frac{612}{\frac{1225}{2}}=\frac{306}{1225}\)
Vậy .. . .
ta co:1/1*2*3=(1/1*2-1/2*3):2
1/2*3*4=(1/1*2-1/2*3):2
...
cu nhu the cho den:
1/98*99*100=(1/98*99-1/99*100):2
suy ra : 1/1*2*3+1/2*3*4+1/3*4*5+...+1/98*99*100
=(1/1*2-1/2*3):2+(1/2*3-1/3*4):2+...+(1/98*99-1/99*100):2
=(1/1*2-1/2*3+1/2*3-1/3*4+...+1/98*99-1/99*100):2
=(1/1*2-1/99*100):2
=(1/2-1/9900)
=(4950/9000-1/9000):2
=4949/9000:2
=4949/18000
học tốt
Tính bằng cách thuận tiện :
\(\frac{1}{1x2}+\frac{1}{2x3}+\frac{1}{3x4}+\frac{1}{4x5}+...+\frac{1}{99x100}\)
Mình sẽ tick cho một bạn nhanh nhất ! ^_^
\(=\frac{1}{1}-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{99}-\frac{1}{100}=1-\frac{1}{100}=\frac{99}{100}\)
Đặt \(M=\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+...+\frac{1}{99.100}\)
\(M=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+...+\frac{1}{99}-\frac{1}{100}\)
\(M=1-\frac{1}{100}\)
\(M=\frac{99}{100}\)
\(\frac{1}{1\times2}+\frac{1}{2\times3}+\frac{1}{3\times4}+\frac{1}{4\times5}+....+\frac{1}{99\times100}\)
\(=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{99}-\frac{1}{100}\)
\(=1-\frac{1}{100}\)
\(=\frac{99}{100}\)
1 . tính nhanh
\(A=\frac{1}{1x2x3}+\frac{1}{2x3x4}+\frac{1}{3x4x5}+...+\frac{1}{36x37x38}+\frac{1}{37x38x39}\)
giúp nha
\(A=\frac{1}{1\times2\times3}+\frac{1}{2\times3\times4}+\frac{1}{3\times4\times5}+...+\frac{1}{36\times37\times38}+\frac{1}{37\times38\times39}\)
\(2A=\frac{2}{1\times2\times3}+\frac{2}{2\times3\times4}+\frac{2}{3\times4\times5}+...+\frac{2}{36\times37\times38}+\frac{2}{37\times38\times39}\)
\(2A=\frac{1}{1\times2}-\frac{1}{2\times3}+\frac{1}{2\times3}-\frac{1}{3\times4}+...+\frac{1}{37\times38}-\frac{1}{38\times39}\)
\(2A=\frac{1}{1\times2}-\frac{1}{38\times39}\)
\(2A=\frac{741}{1482}-\frac{1}{1482}\)
\(2A=\frac{370}{741}\)
\(A=\frac{370}{741}:2=\frac{185}{741}\)
\(\frac{1}{1x2x3}+\frac{1}{2x3x4}+\frac{1}{3x4x5}+....+\frac{1}{37x38x39}\)
\(\frac{1}{1x2x3}+\frac{1}{2x3x4}+\frac{1}{3x4x5}+............+\frac{1}{8x9x10}\)
cái đuôi ak ko hiểu còn cái đầu thì dễ
\(\frac{1}{1.2.3}+\frac{1}{2.3.4}+\frac{1}{3.4.5}+.......+\frac{1}{8.9.10}\)
\(=\frac{1}{2}.\left(\frac{2}{1.2.3}+\frac{2}{2.3.4}+\frac{2}{3.4.5}+......+\frac{2}{8.9.10}\right)\)
\(=\frac{1}{2}.\left(\frac{1}{1.2}-\frac{1}{2.3}+\frac{1}{2.3}-\frac{1}{3.4}+\frac{1}{3.4}-\frac{1}{4.5}+.......+\frac{1}{8.9}-\frac{1}{9.10}\right)\)
\(=\frac{1}{2}.\left(\frac{1}{1.2}-\frac{1}{9.10}\right)=\frac{1}{2}.\left(\frac{1}{2}-\frac{1}{90}\right)=\frac{1}{2}.\frac{22}{45}=\frac{11}{45}\)