United a-z of coefficient

Algebra Level 2

$(-1a^{-1}+2b^2-3c^{-3}+4d^4-……………-25y^{-25}+26z^{26})^\theta$

a,b,c,d,e,……,y,z are variables.

The sum of coefficients in expansion of above expression has 9 digits.

What is the value of $\theta$ ?

Clue: Title of the problem.

This is an original problem and belongs to my set Raju Bhai's creations

1 solution

Rajath Rao
Dec 24, 2017

For any expression, to find sum of coefficients, we need to substitute 1 in variables.

If we substitute 1 in above expression, we get,

$(-1+2-3+4-……-25+26)^\theta$

Sum of even numbers = $n(n+1)=13(13+1)$

Sum of odd numbers= $n^2=13^2$

$(2+4+6…+26)-(1+3+5…+25)=13(13+1)-13^2=13$

Sum of coefficients= $13^\theta$

Given that ,the sum of coefficients has 9 digits.

Therefore, $\boxed{\theta=8}$