Question

The sum of the rational terms in the expansion of (2+31/5)10 is ...

Answer 1

Answer:

Step-by-step explanations

Consider

((3^1/5)+(2^1/3))^30

Here the 1st and last term will be

3^30/5 = 3^6

2^30/3 = 2^10

But you will miss out the 16th term for starting which is

30C15 (3^15/5)(2^15/3) = 30C15 (3^3)(2^5)

Here C is for the combination(as in permutation and combination)

I will try and explain the basic logic behind this,

For any polynomial of type,

(x^1/p + y^1/q)^n

What you need to do is take Common Multiples of p and q and then take corresponding terms from the binomial expansion of the polynomial to get Integral Values