Question

Whats 1/99.100 - 1/99.98 - 1/98.97 - ... - 1/2.1

Answer 1

-9799/9900

Explanation:

1/(99×100) - [1/2.1 + 1/3.2+ ... 1/99.98]

1/2.1 + 1/3.2+ ... 1/99.98

1((n+1)(n) = 1/n - 1/(n+1)

Sum from n=1 till n=98

1/(99×100) - [1 - 1/99]

1/(99×100) - 98/99

(1 - 9800)/9900

-9799/9900