G=1/2.6+1/4.9+1/6.12+.................+1/36.57+1/38.60
H=38/25+9/10-11/15+13/21-15/28+17/36-19/45+....................+197/485-199/4950
Ai giúp mình nhanh nhất mình tick cho.
Giúp mình với: Tính tổng S = 38/25+9/10-11/15+13/21-15/28+17/36-19/45+...-199/4950
S = 38/25 + 9/10-11/15+13/21+15/28+17/36-19/45 +...-199/4950
#)Giải :
\(S=\frac{38}{25}+\frac{9}{10}-\frac{11}{15}+\frac{13}{21}-\frac{15}{28}+\frac{17}{36}-\frac{19}{45}+...-\frac{119}{4950}\)
\(S=\frac{38}{25}+\left(\frac{9}{10}-\frac{11}{15}\right)+\left(\frac{13}{21}-\frac{15}{28}\right) +\left(\frac{17}{36}-\frac{19}{45}\right)+...+\left(\frac{197}{4851}-\frac{199}{4950}\right)\)
Ta thấy :
\(\left(\frac{9}{10}-\frac{11}{15}\right)=\frac{1}{6}=\frac{1}{\left(2.3\right)}=\frac{1}{2}-\frac{1}{3}\)
\(\left(\frac{13}{21}-\frac{15}{28}\right)=\frac{1}{12}=\frac{1}{\left(3.4\right)}=\frac{1}{3}-\frac{1}{4}\)
\(\left(\frac{17}{36}-\frac{19}{45}\right)=\frac{1}{20}=\frac{1}{\left(4.5\right)}=\frac{1}{4}-\frac{1}{5}\)
..........................................................
\(\left(\frac{197}{4851}-\frac{199}{4950}\right)=\frac{1}{2450}=\frac{1}{\left(49.50\right)}=\frac{1}{49}-\frac{1}{50}\)
\(\Rightarrow S=\frac{38}{25}+\left[\left(\frac{1}{2}-\frac{1}{3}\right)+\left(\frac{1}{3}-\frac{1}{4}\right)+\left(\frac{1}{4}-\frac{1}{5}\right)+...+\left(\frac{1}{49}-\frac{1}{50}\right)\right]\)
\(\Rightarrow S=\frac{38}{25}+\left[\frac{1}{2}-\frac{1}{50}\right]\)
\(\Rightarrow S=\frac{38}{25}+\frac{24}{50}\)
\(\Rightarrow S=2\)
#~Will~be~Pens~#
Tính tổng : A=38/25 + 9/10 - 11/15 + 13/21 - 15/28 + 17/36 - ................+197/4851-199/4950
bỏ tạm 38/25 ra
=(9/10-11/15) +(13/21-15/28) +(197/4851-199/4950)
=1/6+1/12+1/20+...+1/49*50=2450
=3-2/2x3+4-3/3x4+5-4/4x5+....50-49/49x50
=1/2-1/3+1/3-...-1/50
1/2-1/50=12/25
=38/25+12/25=50/25
=2
Tính giá trị của biểu thức, tính nhanh nếu có thể:
21) ( 1 + 1/3 ) . ( 1 + 1/8 ) . ( 1 + 1/15 ) . ...... ( 1+ 1/9999)
22) A = \(\frac{38}{25}+\frac{9}{10}-\frac{11}{15}+\frac{13}{21}-\frac{15}{28}+\frac{17}{36}-......+\frac{197}{4851}-\frac{199}{4950}\)
21)
\(\left(1+\dfrac{1}{3}\right).\left(1+\dfrac{1}{8}\right).\left(1+\dfrac{1}{15}\right).....\left(1+\dfrac{1}{9999}\right)\\ =\dfrac{4}{3}.\dfrac{9}{8}.\dfrac{16}{15}.....\dfrac{10000}{9999}\\ =\dfrac{2.2}{1.3}.\dfrac{3.3}{2.4}.\dfrac{4.4}{3.5}.....\dfrac{100.100}{99.101}\\ =\dfrac{2.3.4.....100}{1.2.3.....99}.\dfrac{2.3.4.....100}{3.4.5.....101}\\ =100.\dfrac{2}{101}\\ =\dfrac{200}{101}\)
(x-2)^2=38/25+9/10-11/15+13/21-15/28+17/36-...+197/4851-199/4950
d/ khó lắm đó nha. ai biết minh tích
38/25 + 9/10 - 11/15 + 13/21 - 15/28 + 17/36 - ............. + 197/4851 - 199/4950.
2. ( x + 1 ) + ( x + 4 ) + ( x + 7 ) + ......... + ( x + 28 ) = 155
( x + 1 ) + ( x + 4 ) + ( x + 7 ) + ......... + ( x + 28 ) = 155
<=>(x+x+x...+x)+(1+4+...+28)=155
=>10x+145=155
=>10x=155-145
=>10x=10
=>x=1
Tìm x, biết :
(x - 2)^2 = 38/25 + 9/10 - 11/15 + 13/21 - 15/28 + 17/36 - ..... + 197/4851 - 199/4950
Tìm x:
[x-2]2=38/25+9/10-11/15+13/21-15/28+17/36-...+197/4851-199/4950
38/25+9/10-11/15+13/21-15/28+17/36-19/45+21/55=