Question

1/5x8+1/8x11+1/11x14+...+1/mx(m+3)=101/1540

Answer 1

Lời giải:

$\frac{1}{5\times 8}+\frac{1}{8\times 11}+\frac{1}{11\times 14}+...+\frac{1}{m\times (m+3)}=\frac{101}{1540}$

$\frac{8-5}{5\times 8}+\frac{11-8}{8\times 11}+\frac{14-11}{11\times 14}+...+\frac{(m+3)-m}{m\times (m+3)}=\frac{303}{1540}$

$\frac{1}{5}-\frac{1}{8}+\frac{1}{8}-\frac{1}{11}+\frac{1}{11}-\frac{1}{14}+...+\frac{1}{m}-\frac{1}{m+3}=\frac{303}{1540}$

$\frac{1}{5}-\frac{1}{m+3}=\frac{303}{1540}$

$\frac{1}{m+3}=\frac{1}{5}-\frac{303}{1540}=\frac{1}{308}$

$\Rightarrow m+3=308$

$\Rightarrow m=308-3=305$

Answer 2

Lời giải:

$\frac{1}{5\times 8}+\frac{1}{8\times 11}+\frac{1}{11\times 14}+...+\frac{1}{m\times (m+3)}=\frac{101}{1540}$

$\frac{8-5}{5\times 8}+\frac{11-8}{8\times 11}+\frac{14-11}{11\times 14}+...+\frac{(m+3)-m}{m\times (m+3)}=\frac{303}{1540}$

$\frac{1}{5}-\frac{1}{8}+\frac{1}{8}-\frac{1}{11}+\frac{1}{11}-\frac{1}{14}+...+\frac{1}{m}-\frac{1}{m+3}=\frac{303}{1540}$

$\frac{1}{5}-\frac{1}{m+3}=\frac{303}{1540}$

$\frac{1}{m+3}=\frac{1}{5}-\frac{303}{1540}=\frac{1}{308}$

$\Rightarrow m+3=308$

$\Rightarrow m=308-3=305$