1/5+1/45+1/117+.+1/9797
=1/1×5+1/5×9+1/9×13+.+1/97×101
=1/4 (1-1/5+1/5-1/9+.+1/97-1/101)
=1/4×(1-1/101)
=1/4×100/101
=25/101