A=1/1^2+1/2^2+1/3^2+1/4^2+.....+1/50^2
<1/1.2+1/2.3+1/3.4+1/4.5+.....+1/50.51
=1/1-1/2+1/2-1/3+1/3-1/4+1/4-1/5+.....+1/50-1/51
=1/1-1/51
=50/51
A=1/1^2+1/2^2+1/3^2+...+1/50^2 < 1/1.2 + 1/2.3 + 1/3.4 + ...+1/50.51
A=1 - 1/2+ 1/2 - 1/3+ 1/3 - 1/4 +....+ 1/50 - 1/51
A= 1 - 1/51
A= 50/51
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