Find the value of [1007] + [503(3/4)] + [252(1/8)] + [126(5/16)] + .....
We have
[1007] + [503(3/4)] + [252(1/8)] + [126(5/16)] + .....
= [(2013 + 1)/2] + [(2013 + 2)/4] + [(2013 + 4)/8] + [(2013 + 8)/16] + ....
= 2013