Question

What is the value of the sum $\dfrac {1}{1\cdot 3} \dfrac {1}{3\cdot 5} \dfrac {1}{5\cdot 7} \dfrac {1}{7\cdot 9} \cdots \dfrac {1}{199\cdot 201}$? express your answer as a fraction in simplest form.

Answer 1

The value of the given sum is 1/201.

Step-by-step explanation:

To find the value of the sum

1/(1*3) * 1/(3*5) * 1/(5*7) * 1/(7*9) * ... * 1/(199*201),

we can notice that each term in the numerator is the reciprocal of the product of two consecutive odd numbers, and each term in the denominator is the product of two consecutive odd numbers.

Therefore, all the terms in the numerator and denominator cancel out, except for the first term and the last term.

So, the value of the sum is equal to 1/(1*201), which simplifies to 1/201.