Question

calculati
1/10*11 + 1/11*12 + 1/12*13 + 1/13*14 + 1/14*15

Answer 1

$\frac{1}{10 \times 11} + \frac{1}{11 \times 12} + \frac{1}{12 \times 13} + \frac{1}{13 \times 14} + \frac{1}{14 \times 15} = \frac{1}{110} + \frac{1}{132} + \frac{1}{156} + \frac{1}{182} + \frac{1}{210} = \frac{546 + 455 + 385 + 330 + 286}{60060} = \frac{2002}{60060} = \frac{1}{3}$

Answer 2

1/(10*11) + 1/(11*12) + 1/(12*13) + 1/(13*14) + 1/(14*15)

=(1/10 - 1/11) + (1/11 - 1/12) + (1/12 - 1/13) + (1/13 - 1/14) +(1/14 - 1/15)

=1/10 - 1/15

=(3-2)/30

=1/30