The first term A1 of known sequence {an} is 1, and the point an is 1（ an.an +1) On the image of function y = x / x + 1, we prove that the slope of chord an + 1 increases with the increase of n

The first term A1 of known sequence {an} is 1, and the point an is 1（ an.an +1) On the image of function y = x / x + 1, we prove that the slope of chord an + 1 increases with the increase of n

An( an.an +1) In the function y = x / x + 1 〈 a (n + 1) = an / (an + 1), take the reciprocal 1 / a (n + 1) = 1 / a (n) + 1 〉 1 / a (n + 1) - 1 / a (n) = 1 〉 {1 / a (n)} is the arithmetic sequence, the first term is 1 / A1 = 1, the tolerance is 1 〈 1 / an = 1 + (n-1) = n 〉 an = 1 / N 〉 the slope of the chord Anan + 1 K = [a (n + 2) - A (n + 1)] / [a (n + 1) - A (n