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OG15 OG16 OG17 OG18 OG19 OG20 OG2022
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M is the sum of the reciprocals of the consecutive integers from 201 to 300, inclusive. Which of the following is true?
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If $${a}_{1}={1}$$ and $${a}_{n+1}={1}+\frac{1}{a_n}$$ for all $$n \geq 1$$, what is the value of $${a}_{5}$$ ?
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181215
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What's the median of the sequence $$\frac{1}{π}$$，$$\frac{1}{π}$$-1，$$\frac{1}{π}$$+1，$$\frac{1}{（π-2）^{2}}$$，$$\frac{1}{（π+2）^{2}}$$？
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Three types of aircraft fly three different routes which lengths are related as 1:3:5. The ratio of the amount of fuel burnt over these routes in the same respective order is 5:3:1. What are the ratios of their respective fuel consumption in units of distance per one unit of fuel burnt?
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300难题
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If $$ x\neq 1$$, is y equal to x + 1 ?
1.$$\frac{y-2}{x-1}$$=1
2.$$y^{2}$$ = $$(x+1)^{2}$$
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190124
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$$\frac{1}{(2n-1)!}$$ - $$\frac{1}{(2n+1)!}$$=$$\frac{an^{2}+bn+c}{(2n+1)!}$$,a+b+c=?
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Ready4
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If  is the center of the circle above, what fraction of the circular region is shaded?
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PREP07 Test 2
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{-10, -6, -5, -4, -2.5, -1, 0, 2.5, 4, 6, 7, 10} A number is to be selected at random from the set above. What is the probability that the number selected will be a solution of the equation (x - 5)(x + 10)(2x - 5) = 0 ?
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191222
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As shown in the figure, a circle is inscribed in a square, what's the ratio of the shaded area to the triangle PQR?（π≈3.14）
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191222
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There are 21 songs in a music CD, where two songs are from the same musician James. What is the probability that these two songs are arranged to play on the first two places ?
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OG18-数学分册
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$${1}\over{3}-\frac{1}{3-\frac{1}{3-1}}$$
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OG18-数学分册
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If a =$$ 1 +\frac{1}{4} +\frac{1}{16} + \frac{1}{64} $$and b = $$1+ \frac{1}{4}a$$, then what is the value of a-b?
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OG19-数学分册
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If $$a= 1 + \frac{1}{4} + \frac{1}{16} + \frac{1}{64}$$ and $$ b = 1 + \frac{1}{4}a$$, then what is
the value of $$a - b$$ ?
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190207
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1+x+$$x^{2}$$+$$x^{3}$$+$$x^{4}$$ < $$\frac{1}{1-x}$$? x≠1
1：x < 1
2：x > 0
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OG16 OG17 OG18 OG19 OG20 OG2022
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Is $$x=\frac{1}{y}$$ ?(1) xy = 1(2) $$\frac{1}{xy}=1$$
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Magoosh
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$${1}\over{1+{{1}\over1-\frac{1}{3}}}$$
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$$1+{{1}\over{1}+({{1}\over{1}+\frac{1}{3}})}$$
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200301
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If $$\frac { 1 } { n + 1 } < \frac { 1 } { 31 } + \frac { 1 } { 32 } + \frac { 1 } { 33 } < \frac { 1 } { n }$$, and n is a positive integer, what is the value of n?
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200301 还原机经选题: 数论&代数
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If s = 1/(1+2+3+4)+1/(1+2+3+4+5)+...+1/(1+2+3+...+98+99), what's the range of s?
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$${(5^{8}+1){(5^{4}+1)}{(5^{2}+1)}{(5^{2}-1)}}$$=
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