In the expansion of (512+718)1024, the number of integral terms is
Here, n=1024=210
Now, Tr+1=nCr(512)1024−r(718)r
For Tr+1 to be an integer,
1024−r must be a multiple of 2, or 0.
r must be a multiple of 8, or 0.
When r is a multiple of 8, say r=8k,
1024−r=1024−8k, which is divisible by 2.
Thus, the number of multiples of 8 between 0 and 1024, including 0 is the number of integers in the expansion.
This number is given by 1024÷8 +1=128+1=129