Observe the following sequence: two thirds, three eighths, four fifteenth, five twenty-four, six thirty-five (1) Please write the sixth number (2) according to the above change rule, please write the nth number

Observe the following sequence: two thirds, three eighths, four fifteenth, five twenty-four, six thirty-five (1) Please write the sixth number (2) according to the above change rule, please write the nth number

The numerator is 2,3,4,5,6. The denominator is 3,8,15,24353 = 2 & # 178; - 1,8 = 3 & # 178; - 1,15 = 4 & # 178; - 1,24 = 5 & # 178; - 1,35 = 6 & # 178; - 17 & # 178; - 1 = 49-1 = 48. Therefore, the sixth number is 7 / 48, and the nth number is: (n + 1) &# 178; - 1] of (n + 1) / [n (n + 2) / [n (n + 1) / [n (n + 1) / [n (n + 2]

When x = 2, the value of 2x power + 3x + C is 10. When x = 6, the value of this algebraic expression

x=2
2x²+3x+C
=8+6+C=10
C=-4
So x = 6
The original formula is 2 × 36 + 3 × 6-4 = 86

Find the maximum value of function y = (x + 1) / (xsquare + 5x + 6) (x > - 1)
Using mean inequality to find the best value

Y = (x + 1) / (X & # 178; + 5x + 6) let x + 1 = t > 0, then x = T-1 ｜ y = t / [(t-1) &# 178; + 5 (t-1) + 6] = t / (T & # 178; + 3T + 2) take the reciprocal 1 / y = t + 2 / T + 3 ∵ T > 0 ｜ T + 2 / T ≥ 2 √ (t * 2 / T) = 2 √ 2 if and only if t = 2 / T, t = √ 2, take the equal sign ｜ 1 / Y ≥ 3 + 2 √ 2 ｜ y ≤ 1 / (3 + 2 √ 2) = 3-2