Đáp án: $C=\dfrac19(\dfrac1{1.4.7}-\dfrac1{154.157.160})$
Giải thích các bước giải:
Ta có:
$C=\dfrac1{1. 4. 7. 10}+\dfrac1{4.7.10.13}+...+\dfrac1{151.154.157.160}$
$\to 9C=\dfrac9{1. 4. 7. 10}+\dfrac9{4.7.10.13}+...+\dfrac9{151.154.157.160}$
$\to 9C=\dfrac{10-1}{1. 4. 7. 10}+\dfrac{13-4}{4.7.10.13}+...+\dfrac{160-151}{151.154.157.160}$
$\to 9C=\dfrac1{1.4.7}-\dfrac1{4.7.10}+\dfrac1{4.7.10}-\dfrac1{7.10.13}+...+\dfrac1{151.154.157}-\dfrac1{154.157.160}$
$\to 9C=\dfrac1{1.4.7}-\dfrac1{154.157.160}$
$\to C=\dfrac19(\dfrac1{1.4.7}-\dfrac1{154.157.160})$
