Tính nhanh$E = \frac{1}{2} + \frac{1}{6} + \frac{1}{{12}} + \frac{1}{{20}} + \frac{1}{{30}} + \frac{1}{{42}} + .... + \frac{1}{{110}}$

Phương pháp giải

Đưa về bài toán tử số bằng hiệu hai thừa số ở mẫu số.

Lời giải của GV ufaindo.xyz

$E = \frac{1}{2} + \frac{1}{6} + \frac{1}{{12}} + \frac{1}{{20}} + \frac{1}{{30}} + \frac{1}{{42}} + .... + \frac{1}{{110}}$ $E = \frac{1}{{1 \times 2}} + \frac{1}{{2 \times 3}} + \frac{1}{{3 \times 4}} + \frac{1}{{4 \times 5}} + .... + \frac{1}{{10 \times 11}}$ $E = 1 - \frac{1}{{11}} = \frac{{10}}{{11}}$

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