Cho 3 số a;b;c thỏa mãn a.b.c1Chứng minhfrac{1}{ab+a+1}+frac{b}{bc+b+1}+frac{1}{abc+bc+b}12)CHứng tỏ rằnga1-frac{1}{2}-frac{1}{2^2}-frac{1}{2^3}-....-frac{1}{2^{10}}frac{1}{2^{11}}b1-frac{1}{2^2}-frac{1}{3^2}-frac{1}{4^2}-...-frac{1}{100^2}frac{1}{100}cleft(frac{1}{2^2}-1right).left(frac{1}{3^2}-1right).left(frac{1}{4^2}-1right)...left(frac{1}{100^2}-1right)
Đọc tiếp
Cho 3 số a;b;c thỏa mãn a.b.c=1
Chứng minh
\(\frac{1}{ab+a+1}+\frac{b}{bc+b+1}+\frac{1}{abc+bc+b}=1\)
2)
CHứng tỏ rằng
\(a=1-\frac{1}{2}-\frac{1}{2^2}-\frac{1}{2^3}-....-\frac{1}{2^{10}}>\frac{1}{2^{11}}\)
\(b=1-\frac{1}{2^2}-\frac{1}{3^2}-\frac{1}{4^2}-...-\frac{1}{100^2}>\frac{1}{100}\)
\(c=\left(\frac{1}{2^2}-1\right).\left(\frac{1}{3^2}-1\right).\left(\frac{1}{4^2}-1\right)...\left(\frac{1}{100^2}-1\right)
