Cho S₁=1+\(\frac{1}{5}\);S₂=1+\(\frac{1}{5}+\frac{1}{5^2};...;\)S_n=\(1+\frac{1}{5}+\frac{1}{5^2}+...+\frac{1}{5^n}\left(n\inℕ^∗\right)\)

CMR:1/5S₁²+1/5²S₂²+.

..+1/5ⁿS_n²<1/4