What is 1 / (1 * 3) + 1 / (3 * 5) + 1 / (5 * 7) + --- 1 / (97 * 99)?

1/(1*3)+1/(3*5)+1/(5*7)+----1/(97*99)
=1/2[1-1/3]+1/2[1/3-1/5]+...+1/2[1/97-1/99]
=1/2[1-1/3+1/3-1/5+...+1/97-1/99]
=1/2*[1-1/99]
=1/2*98/99
=49/99

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