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S=1/2+1/4+1/8+1/16+1/32+1/64
S=1-1/2+1/2-1/4+1/4-1/8+1/8-1/16+1/16-1/32+1/32-1/64
S=1-1/64
S=63/64
\(=\frac{1}{1.7}+\frac{1}{7.13}+\frac{1}{13.19}+.......+\frac{1}{31.37}=\frac{1-\frac{1}{37}}{6}\)
=1/1×7+1/7×13+1/13×19+...+1/31×37
=1/6×(1-1/7)+1/6×(1/7-1/13)+1/6×(1/13-1/19)+...+1/6×(1/31-1/37)
=1/6×(1-1/7+1/7-1/13+1/13-1/19+...+1/31-1/37)
=1/6×(1-1/37)
=1/6×36/37
=6/37
Ta có:
\(A=\frac{1}{7}+\frac{1}{91}+\frac{1}{247}+\frac{1}{475}+\frac{1}{775}+\frac{1}{1147}\)
\(=\frac{1}{1.7}+\frac{1}{7.13}+\frac{1}{13.19}+\frac{1}{19.25}+\frac{1}{25.31}+\frac{1}{31.37}\)
\(6A=\frac{6}{1.7}+\frac{6}{7.13}+\frac{6}{13.19}+\frac{6}{19.25}+\frac{6}{25.31}+\frac{6}{31.37}\)
\(=1-\frac{1}{7}+\frac{1}{7}-\frac{1}{13}+\frac{1}{13}-\frac{1}{19}+\frac{1}{19}-\frac{1}{25}+\frac{1}{25}-\frac{1}{31}+\frac{1}{31}-\frac{1}{37}\)
\(=1-\frac{1}{37}=\frac{36}{37}\)
\(A=\frac{6}{37}\)
