tính nhanh:
1/3 + 13/15 + 33/35 + 61/63 + 97/99 + 141/143
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7 tháng 10 2020
\(A=1-\frac{2}{3}+1-\frac{2}{15}+1-\frac{2}{35}+1-\frac{2}{63}+1-\frac{2}{99}+1-\frac{2}{143}\)
\(=1+1+1+1+1+1-\frac{2}{3}-\frac{2}{15}-\frac{2}{35}-\frac{2}{63}-\frac{2}{99}-\frac{2}{143}\)
\(=6-\left(\frac{2}{3}+\frac{2}{15}+\frac{2}{35}+\frac{2}{63}+\frac{2}{99}+\frac{2}{143}\right)\)
\(=6-\left(\frac{1}{1}-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+...+\frac{1}{11}-\frac{1}{13}\right)\)
\(=6-\left(1-\frac{1}{13}\right)\)
\(=6-1+\frac{1}{13}\)
\(=5+\frac{1}{13}\)
\(=\frac{65}{13}+\frac{1}{13}\)
\(=\frac{66}{13}\)
NN
1
1 tháng 7 2016
\(\frac{1}{3}+\frac{13}{15}+\frac{33}{35}+\frac{61}{63}+\frac{97}{99}+\frac{141}{143}\)
\(=\left(1-\frac{2}{3}\right)+\left(1-\frac{2}{15}\right)+\left(1-\frac{2}{35}\right)+\left(1-\frac{2}{63}\right)+\left(1-\frac{2}{99}\right)+\left(1-\frac{2}{143}\right)\)
\(=\left(1+1+1+1+1+1\right)-\left(\frac{2}{3}+\frac{2}{15}+\frac{2}{35}+\frac{2}{63}+\frac{2}{99}+\frac{2}{143}\right)\)
\(=6-\left(\frac{2}{1.3}+\frac{2}{3.5}+\frac{2}{5.7}+\frac{2}{7.9}+\frac{2}{9.11}+\frac{2}{11.13}\right)\)
\(=6-\left(1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+\frac{1}{9}-\frac{1}{11}+\frac{1}{11}-\frac{1}{13}\right)\)
\(=6-\left(1-\frac{1}{13}\right)\)
\(=6-\frac{12}{13}\)
\(=\frac{66}{13}\)
Ủng hộ mk nha ^_-
NN
10 tháng 5 2022
C=1-2/15+1-2/35+1-2/63+...+1-2/195
\(C=6-\left(\dfrac{2}{3x5}+\dfrac{2}{5x7}+\dfrac{2}{7x9}+...+\dfrac{2}{13x15}\right)=\)
\(=6-\left(\dfrac{5-3}{3x5}+\dfrac{7-5}{5x7}+\dfrac{9-7}{7x9}+...+\dfrac{15-13}{13x15}\right)=\)
\(=6-\left(\dfrac{1}{5}-\dfrac{1}{7}+\dfrac{1}{7}-\dfrac{1}{9}+\dfrac{1}{9}-\dfrac{1}{11}+...+\dfrac{1}{13}-\dfrac{1}{15}\right)=\)
\(=6-\left(\dfrac{1}{5}-\dfrac{1}{15}\right)=\dfrac{88}{15}\)
XO
26 tháng 9 2019
A = \(\frac{1}{3}+\frac{13}{35}+\frac{33}{35}+\frac{61}{63}+\frac{97}{99}+\frac{141}{143}\)
\(=\left(1-\frac{2}{3}\right)+\left(1-\frac{2}{15}\right)+\left(1-\frac{2}{35}\right)+\left(1-\frac{2}{63}\right)+\left(1-\frac{2}{99}\right)+\left(1-\frac{2}{143}\right)\)
\(=\left(1+1+1+1+1+1\right)-\left(\frac{2}{3}+\frac{2}{15}+\frac{2}{35}+\frac{2}{63}+\frac{2}{99}+\frac{2}{143}\right)\)
\(=6-\left(\frac{2}{1.3}+\frac{2}{3.5}+\frac{2}{5.7}+\frac{2}{7.9}+\frac{2}{9.11}+\frac{2}{11.13}\right)\)
\(=6-\left(1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+\frac{1}{9}-\frac{1}{11}+\frac{1}{11}-\frac{1}{13}\right)\)
\(=6-\left(1-\frac{1}{13}\right)\)
\(=6-1+\frac{1}{13}\)
\(=5+\frac{1}{13}\)
\(=\frac{66}{13}\)
\(\text{Vậy }A=\frac{66}{13}\)
31 tháng 7 2015
Ta có: \(A=\frac{3-2}{3}+\frac{15-2}{15}+\frac{35-2}{35}+\frac{63-2}{63}+\frac{99-2}{99}+\frac{143-2}{143}+\frac{195-2}{195}\)
\(A=\left(1-\frac{2}{3}\right)+\left(1-\frac{2}{15}\right)+\left(1-\frac{2}{35}\right)+\left(1-\frac{2}{63}\right)+\left(1-\frac{2}{99}\right)+\left(1-\frac{2}{143}\right)+\left(1-\frac{2}{195}\right)\)
\(A=7-\left(\frac{2}{3}+\frac{2}{15}+\frac{2}{35}+\frac{2}{63}+\frac{2}{99}+\frac{2}{143}+\frac{2}{195}\right)\)
\(A=7-\left(\frac{2}{1.3}+\frac{2}{3.5}+\frac{2}{5.7}+\frac{2}{7.9}+\frac{2}{9.11}+\frac{2}{11.13}+\frac{2}{13.15}\right)\)
\(A=7-\left(1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+\frac{1}{9}-\frac{1}{11}+\frac{1}{11}-\frac{1}{13}+\frac{1}{13}-\frac{1}{15}\right)\)
\(A=7-\left(1-\frac{1}{15}\right)=7-1+\frac{1}{15}=6\frac{1}{15}\)không là số nguyên
25 tháng 5 2018
Đ/S: \(\frac{45}{11}\)
k đúng cho mình nha!!
chúc bạn hk tốt nhé!!
NP
1
1 tháng 4 2023
\(\dfrac{1}{3}+\dfrac{13}{15}+\dfrac{33}{35}+\dfrac{61}{63}+\dfrac{97}{99}\)
\(=\left(1-\dfrac{2}{3}\right)+\left(1-\dfrac{2}{15}\right)+\left(1-\dfrac{2}{35}\right)+\left(1-\dfrac{2}{63}\right)+\left(1-\dfrac{2}{99}\right)\)
\(=\left(1+1+1+1+\right)-\left(\dfrac{2}{3}+\dfrac{2}{15}+\dfrac{2}{35}+\dfrac{2}{63}+\dfrac{2}{99}\right)\)
\(=5-\left(\dfrac{2}{1.3}+\dfrac{2}{3.5}+\dfrac{2}{5.7}+\dfrac{2}{7.9}+\dfrac{2}{9.11}\right)\)
\(=5-\left(1-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{7}+...+\dfrac{1}{9}-\dfrac{1}{11}\right)\)
\(=5-\left(1-\dfrac{1}{11}\right)\)
\(=5-\dfrac{10}{11}\)
\(=\dfrac{45}{11}\)
\(\frac{1}{3}+\frac{13}{15}+\frac{33}{35}+\frac{61}{63}+\frac{97}{99}\)\(+\frac{141}{143}\)
\(=\left(1-\frac{2}{3}\right)+\left(1-\frac{2}{15}\right)\)\(+\left(1-\frac{2}{35}\right)+\left(1-\frac{2}{63}\right)\)\(+\left(1-\frac{2}{99}\right)+\left(1-\frac{2}{143}\right)\)
\(=\left(1+1+1+1+1+1\right)-\)\(\left(\frac{2}{3}+\frac{2}{15}+\frac{2}{35}+\frac{2}{63}+\frac{2}{99}+\frac{2}{143}\right)\)
\(=6-\)\(\left(\frac{2}{1\times3}+\frac{2}{3\times5}+\frac{2}{5\times7}+\frac{2}{7\times9}+\frac{2}{9\times11}+\frac{2}{11\times13}\right)\)
\(=6-\)\(\left(1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+\frac{1}{9}-\frac{1}{11}+\frac{1}{11}-\frac{1}{13}\right)\)
\(=6-\left(1-\frac{1}{13}\right)\)
\(=6-\frac{12}{13}\)
\(=\frac{66}{13}\)