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

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

Grade:12

2 Answers

Siddharth Singh
22 Points
6 years ago
I’m sorry I’ve done it now.. 
But I will answer anyway.. 
 
Write the general term. 
Tr+1= 1024Cr.(51/2)1024-r.(71/8)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
Siddharth Singh
22 Points
6 years ago
I’m sorry I’ve done it now.. 
But I will answer anyway.. 
 
Write the general term. 
Tr+1= 1024Cr.(51/2)1024-r.(71/8)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

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