Tính : 1/3 + 1/15 + 1/35 + … + 1/399 + 1/483
Tính : 1/2 – 1/3 – 1/9 – …- 1/729 – 1/2187
Tính : 10^2 + 11^2 + 12^2 + … + 20^2
Tính : 1/3 + 1/15 + 1/35 + … + 1/399 + 1/483
Tính : 1/2 – 1/3 – 1/9 – …- 1/729 – 1/2187
Tính : 10^2 + 11^2 + 12^2 + … + 20^2
*$\frac{1}{3}$+$\frac{1}{15}$+$\frac{1}{35}$+…+$\frac{1}{339}$+$\frac{1}{483}$
=$\frac{1}{1.3}$+$\frac{1}{3.5}$+$\frac{1}{5.7}$+…+$\frac{1}{19.21}$+$\frac{1}{21.23}$
=$1-$$\frac{1}{3}$+$\frac{1}{3}$-$\frac{1}{5}$+$\frac{1}{5}$-$\frac{1}{7}$+…+$\frac{1}{19}$- $\frac{1}{21}$+$\frac{1}{21}$-$\frac{1}{23}$
=$1$-$\frac{1}{23}$
=$\frac{22}{23}$
*Đặt A=$\frac{1}{2}$-$\frac{1}{3}$-$\frac{1}{9}$-…-$\frac{1}{729}$-$\frac{1}{2187}$
A=$\frac{1}{2}$-$\frac{1}{3^1}$-$\frac{1}{3^2}$-…-$\frac{1}{3^6}$-$\frac{1}{3^7}$
$\frac{1}{3}$A=$\frac{1}{2}$-$\frac{1}{3}$.($\frac{1}{3^1}$-$\frac{1}{3^2}$-…-$\frac{1}{3^6}$-$\frac{1}{3^7}$)
$\frac{1}{3}$A=$\frac{1}{2}$-($\frac{1}{3^2}$-$\frac{1}{3^3}$-…-$\frac{1}{3^7}$-$\frac{1}{3^8}$)
A-$\frac{1}{3}$A=$\frac{1}{2}$-($\frac{1}{3^1}$-$\frac{1}{3^2}$-…-$\frac{1}{3^6}$-$\frac{1}{3^7}$)-
($\frac{1}{3^2}$-$\frac{1}{3^3}$-…-$\frac{1}{3^7}$-$\frac{1}{3^8}$)
$\frac{2}{3}$A=$\frac{1}{2}$-$\frac{1}{3}$-$\frac{1}{3^8}$
A=$\frac{2185}{13122}$:$\frac{2}{3}$
A=$\frac{2185}{8748}$
*$10^2 + 11^2 + 12^2 + … + 20^2$
$=100+121+144+169+196+225+256+289+324+361+400$
$=(100+400)+(121+169+289+361)+(144+196+256+324)+225$
$=500+940+920+225$
$=2585$
Câu 1:
1/3+1/15+…+1/483
=1/1×3+1/3×5+1/21×23
=1/1-1/3+1/3-1/5+…+1/21-1/23
=1-1/23
=22/23
Câu 2:
Ta đặt dãy tính trên bằng A
Ta có:
A= 1/3 + 1/9 + 1/27 + 1/81 + 1/243 + 1/729 + 1/2187
Nhân A với 3 , ta có :
A x 3 = 3x ( 1/3 + 1/9 + 1/27 + 1/81 + 1/243 + 1/729 + 1/2187)
A x 3 = 1+ ( 1/3 + 1/9 + 1/27 + 1/81 + 1/243 + 1/729)
A x 3 = 1 + A – 1/2187
A x 2 = 1 – 1/2187
A x 2 = 2186 / 2187
A = 2186 / 2187 : 2
A = 1093/2187
Vậy kết quả của dãy tính trên là 1093/2187
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