It is known that the general term formula of {an} is an = n / (n ^ 2 + 196), and the maximum value of {an} can be obtained It is known that the general formula of {an} is an = n / (n ^ 2 + 196), (n is a positive integer) to find the maximum value of {an}

An = n / (n ^ 2 + 196), (n is a positive integer)
An = 1 / (n + 196 / N) ≤ 1 / [2 * radical (n * 196 / N)] = 1 / 28
So the maximum value of {an} is 1 / 28

N the general term formula of known sequence an is an = n + 10 / 2n + 1, TN is the first N-term product of sequence an, when TN reaches the maximum, the value of n is?
10 + n ≥ 2n + 1 when n = 9
This T8 = T9, so n can take 8 9

When the numerator is greater than the denominator, the value of the fraction is greater than 1. When the numerator multiplies the fraction greater than 1, the product will increase. When the numerator multiplies the fraction less than 1, the product will decrease. Therefore, TN = a1a2a3. If an wants to get the maximum value, it will get the maximum value when an is just close to or equal to 1

In the sequence {an}, an = 23-2n, then when n is the value, the first n terms and Sn of the sequence get the maximum value? What is the maximum value?

∵ A1 = 21, an + 1-an = - 2, is an arithmetic sequence, so Sn = (21 + 23 − 2n) × N2 = 22n − N2 = − (n − 11) 2 + 121. According to the properties of quadratic function, when n = 11, Sn takes the maximum value, which is 121

It is known that the general term formula of {an} is an = n / (n ^ 2 + 196), and the maximum value of {an} can be obtained It is known that the general formula of {an} is an = n / (n ^ 2 + 196), (n is a positive integer) to find the maximum value of {an}