A = `1/$2^{2}$` + `1/$3^{2}$` + ... + `1/$150^{2}$`
Ta thấy :
`1/$2^{2}$` < $\frac{1}{1.2}$ = 1 = `1/2`
`1/$3^{2}$` < $\frac{1}{2.3}$ = `1/2` - `1/3`
...................
`1/$150^{2}$` < $\frac{1}{149.150}$ = `1/149` - `1/150`
=> A < $\frac{1}{1.2}$ + $\frac{1}{2.3}$ + ... + $\frac{1}{149.150}$
=> A < 1 - `1/2` + `1/2` - `1/3` + ... + `1/149` - `1/150`
=> A < 1 - `1/150`
Vì 1 - `1/150` < 1
=> A < 1.
