Number of Integral terms in expansion of (5^1/2 + 7^1/8)^1024 ?

I’m sorry I’ve done it now.. 

But I will answer anyway.. 

 

Write the general term. 

Tr+1= 1024Cr.(5^1/2)^1024-r.(7^1/8)^r

Now 1024Cr is always an integer.. 
 

We have to check for (1024-r)/2 and r/8 to be integer. .we can see that the no has to be divisble by 8 and yet it has to be an even number too... 
Simply we see the maximum multipliation of 8 for which it is valid which is 129... because 8*130=1040.

Thank you

I’m sorry I’ve done it now.. 

But I will answer anyway.. 

 

Write the general term. 

Tr+1= 1024Cr.(5^1/2)^1024-r.(7^1/8)^r

Now 1024Cr is always an integer.. 
 

We have to check for (1024-r)/2 and r/8 to be integer. .we can see that the no has to be divisble by 8 and yet it has to be an even number too... 
Simply we see the maximum multipliation of 8 for which it is valid which is 129... because 8*130=1040.

Thank you