Inequality expansion and contraction. Do it before tomorrow morning, add 50 points. Prove: 1 / 2n ^ 2 + 3N + 1 is less than 5 / 12, the front 2n ^ 2 + 3N + 1 is the denominator It is proved that 1 / 2n ^ 2 + 3N + 1 is less than 5 / 12 N, and 2n ^ 2 + 3N + 1 before N + is the denominator Sum.

Inequality expansion and contraction. Do it before tomorrow morning, add 50 points. Prove: 1 / 2n ^ 2 + 3N + 1 is less than 5 / 12, the front 2n ^ 2 + 3N + 1 is the denominator It is proved that 1 / 2n ^ 2 + 3N + 1 is less than 5 / 12 N, and 2n ^ 2 + 3N + 1 before N + is the denominator Sum.

1/(2n^2+3n+1)
=1/[(2n+1)(n+1)]=2*1/[(2n+1)(2n+2)]=2[1/(2n+1)-1/(2n+2)]
Sum = 2 (1 / 3-1 / 4 + 1 / 5-1 / 6 + 1 / 7...)
A = 1 / 3-1 / 4 + 1 / 5-1 / 6 + 1 / 7
a=1/3-1/4+(1/5-1/6)+(1/7-1/8)+.
1/[(n+1)(n+2)]
=1/(n+1)-1/(n+2) )
=1/12+(1/3-a)
So 2A