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Q.
In every term, the sum of indices of $a$ and $b$ in the expansion of $(a+b)^n$ is
Binomial Theorem
Solution:
In the expansion of $(a+b)^n$, the sum of the indices of $a$ and $b$ is $n+0=n$ in the first term, $(n-1)+1=n$ in the second term and so on $0+n=n$ in the last term.
Thus, it can be seen that the sum of the indices of $a$ and $b$ is $n$ in every term of the expansion.