Bạn xem đã viết đúng đề chưa nhỉ. Các thừa số đang cách nhau 3 đơn vị tự nhiên xuất hiện 7 x 11 có 2 thừa số cách nhau 4 đơn vị?
S = \(\dfrac{3}{1.4}\) + \(\dfrac{3}{4.7}\) + \(\dfrac{3}{7.11}\) + \(\dfrac{3}{11.14}\) + \(\dfrac{3}{14.17}\)
S = \(\dfrac{3}{1.4}\) + \(\dfrac{3}{4.7}\) + \(\dfrac{4}{7.11}\) - \(\dfrac{1}{7.11}\) + \(\dfrac{3}{11.14}\) + \(\dfrac{3}{14.17}\)
S = \(\dfrac{3}{1.4}\) + \(\dfrac{3}{4.7}\) + \(\dfrac{4}{7.11}\) + \(\dfrac{3}{11.14}\) + \(\dfrac{3}{14.17}\) - \(\dfrac{1}{7.11}\)
S = \(\dfrac{1}{1}\) - \(\dfrac{1}{4}\) + \(\dfrac{1}{4}\) - \(\dfrac{1}{7}\) + \(\dfrac{1}{7}\) - \(\dfrac{1}{11}\) + \(\dfrac{1}{11}\) - \(\dfrac{1}{14}\) + \(\dfrac{1}{14}\) - \(\dfrac{1}{17}\) - \(\dfrac{1}{77}\)
S = \(\dfrac{1}{1}\) - \(\dfrac{1}{17}\) - \(\dfrac{1}{77}\)
S = \(\dfrac{16}{17}\) - \(\dfrac{1}{77}\)
S = \(\dfrac{1215}{1309}\)
