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Công thức : (số cuối +số đầu)x số số hạng:2
Giải :
Số số hạng của dãy là:(16836-1):1+1=16836
Tổng là:(1+16836)x16836:2=141733866
Duyệt nha!
Ta có : \(\frac{49}{5}-\frac{1}{2}-\frac{1}{4}-\frac{1}{8}-\frac{1}{16}-\frac{1}{32}\)
\(=\frac{49}{5}-\left(\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}+\frac{1}{32}\right)\)
Đặt \(A=\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}+\frac{1}{32}\)
=> \(2A=1+\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}\)
=> \(2A-A=1-\frac{1}{32}\Rightarrow A=\frac{31}{32}\)
Vậy \(\frac{49}{5}-\frac{1}{2}-\frac{1}{4}-\frac{1}{8}-\frac{1}{16}-\frac{1}{32}\)
\(=\frac{49}{5}-\frac{31}{32}=\frac{1413}{160}\)
\(\frac{49}{5}-\frac{1}{2}-\frac{1}{4}-\frac{1}{8}-\frac{1}{16}-\frac{1}{32}\)\(=\)\(\frac{4189}{480}\)
a. \(\dfrac{17}{13}-\dfrac{14}{23}+\dfrac{9}{13}-\dfrac{9}{23}=\left(\dfrac{17}{13}+\dfrac{9}{13}\right)-\left(\dfrac{14}{23}+\dfrac{9}{23}\right)=\dfrac{26}{13}-\dfrac{23}{23}=2-1=1\)
b.\(\dfrac{49}{5}-\dfrac{1}{2}-\dfrac{1}{4}-\dfrac{1}{32}-\dfrac{1}{16}-\dfrac{1}{32}=\dfrac{49}{5}-\left(1-\dfrac{1}{32}\right)=\dfrac{44}{5}+\dfrac{1}{32}=\dfrac{1413}{160}\)
A=1-1/2+1/2-1/4+1/4-1/8+1/8-1/16+1/16-1/32+1/32-1/64
A=1- bạn gạch chéo từ 1/2(đầu tiên) đến 1/32 nha
A=1-1/64=65/64.
B=Bạn làm tương tự như trên nha
k mik nha. Thanks. Chúc bạn học tốt!!!
a) A=1/2 + 1/4 + 1/8 + 1/16 + 1/32 + 1/64
2A=1+1/2+1/4 + 1/8 + 1/16 + 1/32
2A-A= 1+1/2+1/4+1/8+1/16+1/32-(1/2+1/4+1/8+1/16+1/32+1/64)
A= 1-1/64=63/64
b) B= 1/4+1/8+1/16+......+1/512
2B= 1/2+1/4+1/8+1/16+......+1/256
2B-B=1/2+1/4+1/8+1/16+.....+1/256-(1/4+1/8+1/16+.....+1/512)
B=1/2-1/512=255/512
1/2 + 1/4 + 1/8 + 1/16+ 1/32 + 1/64 + 1/128
= 64/ 128 + 32/128 + 16/128 +8/128 + 4/128 +2/128 + 1/128
= ( 64 + 32 + 16 + 8 + 4 + 2 + 1 ) /128
= 127/ 128
= 1 - 1/2 + 1/2 - 1/4 + 1/4 - ............ + 1/64 - 1/128
= 1 - 1/128
= 127/128
k nha bn
Đặt A=1/2+1/4+1/8+1/16+1/32
2A=1+1/2+1/4+1/8+1/16
Ta có:
2A-A=1+1/2+1/4+1/8+1/16-(1/2+1/4+1/8+1/16+1/32)
A=1-1/32=31/32
Ta đặt :
\(A=\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}+\frac{1}{32}\)
\(A\cdot2=\left(\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}+\frac{1}{32}\right)\cdot2\)
\(A\cdot2=\frac{1}{2}\cdot2+\frac{1}{4}\cdot2+\frac{1}{8}\cdot2+\frac{1}{16}\cdot2+\frac{1}{32}\cdot2\)
\(A\cdot2=1+\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}\)
\(A\cdot2-A=\left(1+\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}\right)-\left(\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}+\frac{1}{32}\right)\)
\(A=1-\frac{1}{32}\)
\(A=\frac{31}{32}\)
\(A=\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}+\frac{1}{32}\)
\(A=\frac{1}{2^1}+\frac{1}{2^2}+\frac{1}{2^3}+\frac{1}{2^4}+\frac{1}{2^5}\)
\(2A=1+\frac{1}{2}+\frac{1}{2^2}+\frac{1}{2^3}+\frac{1}{2^4}\)
\(2A-A=1-\frac{1}{2^5}\)
\(A=\frac{32}{32}-\frac{1}{32}\)
\(A=\frac{31}{32}\)
tính nhanh
49/5-1/2-1/4-1/8-1/16-1/32=8,83125
nha bn duyệt đi
\(\frac{49}{5}-\frac{1}{2}-\frac{1}{4}-\frac{1}{8}-\frac{1}{16}-\frac{1}{32}=\frac{1413}{160}=8,83125\)