Problem #PRU-60427

Find the sums of the following series:

a) $\frac{1}{1 \times 2} + \frac{1}{2 \times 3} + \frac{1}{3 \times 4} + \frac{1}{4 \times 5} + \dots$ ;

b) $\frac{1}{1 \times 2 \times 3} + \frac{1}{2 \times 3 \times 4} + \frac{1}{3 \times 4 \times 5} + \frac{1}{4 \times 5 \times 6} + \dots$ ;

c) $\frac{0!}{r!} + \frac{1!}{(r - 1)!} + \frac{2!}{(r - 2)!} + \frac{3!}{(r - 3)!} + \dots$ for $r \geq 2$ .

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