Let the inequality 2 ^ n > n ^ 2 + 1 hold for any natural number n ≥ K. The minimum K value is__________

Let the inequality 2 ^ n > n ^ 2 + 1 hold for any natural number n ≥ K. The minimum K value is__________

When 2 ^ n > n ^ 2 + 1 (1) n = 0, (1) is not tenable; when n = 1, (1) is not tenable; when n = 2, (1) is not tenable; when n = 3, (1) is not tenable; when n = 4 (1) is not tenable; when n = 5 (1) is tenable (32 > 26), let n = k > 4, (1) be tenable

Let s = 1 * 2 * n + (4K + 3), n be greater than or equal to 3, and K be a natural number between 1 and 100. S is a complete square number. How many values of K are there?

If n > = 4 1 * 2 * n must be divisible by 4, so the right side must be divided by 4 and the remainder 3, and S is a complete square number. If s is an even square number, then s can be divisible by 4. If s is an odd square number, then s = (2m + 1) & # 178; = 4m & # 178; + 4m + 1 is divisible by 4 and the remainder 1, so the left side must not equal to the right side, so n = 3 1 * 2 * n =

We know that f (n) = K (n is a natural number), where k is 0.9196461178 If f (1) = 9, f (2) = 1, f (3) = 9, f (4) = 6, then 5F {… F [f (5)]} 555 F + 8F {… F [f (8)]} 888 f=______ ．

Because f (5) = 4, f (4) = 6, f (6) = 6 ，5f{… f[f（5）]}=5×6=30，f（8）=1，f（1）=9，f（9）=7，f（7）=1，f（1）=9，f（9）=7，… 888÷3=296，8f{… If f [f (8)]} = 8 × 7 = 56, then 5F { f[f（5）]}+8f{… F [f (8)]} = 30 + 56 = 86