Cho A = ($\frac{1}{2^{2} }$ – 1 ) . ($\frac{1}{3^{2} }$ – 1) . ($\frac{1}{4^{2} }$ – 1) … ($\frac{1}{40^{2} }$ – 1) so sánh A với -$\frac{1}{2}$
Cho A = ($\frac{1}{2^{2} }$ – 1 ) . ($\frac{1}{3^{2} }$ – 1) . ($\frac{1}{4^{2} }$ – 1) … ($\frac{1}{40^{2} }$ – 1) so sánh A với -$\frac{1}{2}$
By Genesis
A=(1/2^2-1).(1/3^2-1).(1/4^2-1)….(1/40^2-1)
⇒A=-3/4 . -8/9 . -15/16 …. -1599/1600
⇒A=1.(-3).2.(-4).3.(-5)….39.(-41)/2.2.3.3.4.4…..40.40
⇒A=1.2.3…39/2.3.4….40 – (-3).(-4).(-5)….(-41)/2.3.4…40
⇒A=1/40 – -41/2
⇒A=1/40 + 41/2
⇒A= 821/40
Ta có 821/40 > 1
Mà 1/2<1
⇒821/40>1/2
⇒A>1/2