It is known that for any natural number n, the inequality (nlga0) holds, then the value range of a is It is known that for any natural number n, the inequality NLGA ＜ (n + 1) LGA ^ n (a > 0) holds, then the value range of a is () A 0＜a＜1 B a＞1 C 0 < a < 1 / 2 d 0 < a < 1 / 2 or a > 1 Why D

It is known that for any natural number n, the inequality (nlga0) holds, then the value range of a is It is known that for any natural number n, the inequality NLGA ＜ (n + 1) LGA ^ n (a > 0) holds, then the value range of a is () A 0＜a＜1 B a＞1 C 0 < a < 1 / 2 d 0 < a < 1 / 2 or a > 1 Why D

(n + 1) LGA ^ n does it mean (n + 1) times the logarithm of the nth power of a with base 10? If so, the option given in this question is wrong
Solution: move the term to the left and simplify it to 00, so a > 1
(it is worth noting that the natural number here does not include 0)

What is the sum of all the natural numbers n suitable for inequality 7 / 18 < n / 5 < 20 / 7
Please list the formula,

The inequality terms are multiplied by 18 * 5 * 7 at the same time
Score: 245

The known inequality 1 / (n + 1) + 1 / (n + 2) +... 1 / 2n > = 1 / 12loga (A-1) + 2 / 3 holds for integer n greater than 1, and the range of a is obtained

Let an = 1 / (n + 1) + 1 / (n + 2) +... 1 / 2n, then a (n + 1) - an = 1 / (2n + 1) + 1 / (2n + 2) - 1 / (n + 1) = 1 / (2n + 1) - 1 / (2n + 2) > 0, that is, an is an increasing sequence, and 1 / (n + 1) + 1 / (n + 2) +... 1 / 2n > = 1 / 12loga (A-1) + 2 / 3 holds for integer n greater than 1