chọn câu trả lời đúng:
Tính A biết A=12+16+112+...+16480A=12+16+112+...+16480
A A=7881A=7881
B A=7981A=7981
C A=7781A=7781
D A=8081A=8081
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Đáp án cần chọn là: D
A = 1 2 + 1 6 + 1 12 + … + 1 99.100 A = 1 1.2 + 1 2.3 + 1 3.4 + ... + 1 99.100 A = 1 − 1 2 + 1 2 − 1 3 + 1 3 − 1 4 + ... + 1 99 − 1 100 A = 1 − 1 100 = 99 100
So sánh A với 3 5 và 4 5
Ta có
3 5 = 60 100 ; 4 5 = 80 100 ⇒ 60 100 < 80 100 < 99 100 ⇒ A > 4 5 > 3 5
a) 1 5 + 2 5 = 1 + 2 5 = 3 5
b) 3 × 1 2 = 3 × 1 2 = 3 2
c) 1 - 2 3 + 1 6 = 1 - 12 18 + 3 18 = 1 - 15 18 = 3 18 = 1 6
d) 1 1 5 ÷ 1 1 2 = 6 5 ÷ 3 2 = 12 15 = 4 5
e) 3 5 + 2 5 × 1 6 = 3 5 + 2 30 = 20 30 = 2 3
a) 1 5 + 2 5 = 1 + 2 5 = 3 5
b) 3 × 1 2 = 3 × 1 2 = 3 2
c) 1 - 2 3 + 1 6 = 1 - 12 18 + 3 18 = 1 - 15 18 = 3 18 = 1 6
d) 1 1 5 ÷ 1 1 2 = 6 5 ÷ 3 2 = 12 15
e) 3 5 + 2 5 × 1 6 = 3 5 + 2 30 = 20 30 = 2 3
`@` `\text {Ans}`
`\downarrow`
\(\text{ A = }\dfrac{1}{4\times8}+\dfrac{1}{8\times12}+\dfrac{1}{12\times16}+...+\dfrac{1}{172\times176}\)
\(\text{A = }\dfrac{1}{4}\times\left(\dfrac{4}{4\times8}+\dfrac{4}{12\times16}+...+\dfrac{4}{172\times176}\right)\)
\(\text{A = }\dfrac{1}{4}\times\left(\dfrac{1}{4}-\dfrac{1}{8}+\dfrac{1}{12}-\dfrac{1}{16}+...+\dfrac{1}{172}-\dfrac{1}{176}\right)\)
\(\text{A = }\dfrac{1}{4}\times\left(\dfrac{1}{4}-\dfrac{1}{176}\right)\)
\(\text{A = }\dfrac{1}{4}\times\dfrac{43}{176}\)
\(\text{A = }\dfrac{43}{704}\)
Đáp số: `\text {A =} 43/704.`
A = 1/4 x 8 + 1/8 x 12 + 1/12 x 16 + ... + 1/176 x 180
=> 4A = 4/4 x 8 + 4/8 x 12 + 4/12 x 16 + ... + 4/176 x 180
=> 4A = 1/4 - 1/8 + 1/8 - 1/12 + 1/12 - 1/16 + ... 1/176 - 1/180
=> 4A = 1/4 - 1/180
=> 4A = 45/180 - 1/180
=> 4A = 44/180
=> 4A = 11/45
=> A = 11/45 : 4
=> A = 11/180
Vậy A = 11/180
A = \(\dfrac{1}{4\times8}\) + \(\dfrac{1}{8\times12}\) + \(\dfrac{1}{12\times16}\) +...+ \(\dfrac{1}{176\times180}\)
A = \(\dfrac{1}{4}\) \(\times\)( \(\dfrac{4}{4\times8}\)+ \(\dfrac{4}{12\times16}\)+...+ \(\dfrac{4}{176\times180}\))
A = \(\dfrac{1}{4}\) \(\times\)( \(\dfrac{1}{4}\) - \(\dfrac{1}{8}\) + \(\dfrac{1}{12}\) - \(\dfrac{1}{16}\) +...+ \(\dfrac{1}{176}\) - \(\dfrac{1}{180}\))
A = \(\dfrac{1}{4}\) \(\times\)(\(\dfrac{1}{4}\) - \(\dfrac{1}{180}\))
A = \(\dfrac{1}{4}\) \(\times\)\(\dfrac{11}{45}\)
A = \(\dfrac{11}{180}\)