Find the reduced sum of 1/4 + 1/28 +1/70 + 1/130 + 1/208 + 1/304, of course without a calculator

The lucid math content, treating telescoping sums(expressions where significant cancellation of terms leads to favorable simplification), created by Alexander Bogomolny inspired this simple looking problem which is quite tedious if one just tries to work with a huge 6 digit Least Common Denominator. He is well known for his educational web site CTK or Cut the Knot and his passion overcoming deafness impressing all! Thanks to Sabena Singh and Emily Quesnelle for the vital role they play with respect to financial support for disadvantaged Canadians(both math students and other marginalized members of society).
Medium writer Nassim Nicholas Taleb's reportage on the broad and fascinating field of mathematics is transparently and engagingly presented! However, his perception on what constitutes factual information is somewhat suspect. Gotta love the dude's chess insights/commentary!