$\frac{1}{b+c}, \frac{1}{c+a},\frac{1}{a+b}$ are in HP, then which of the following is/are correct?

1. a, b, c are in AP

2. (b + c)², (c + a)², (a + b)² are in GP. Select the correct answer using the code given below.

$\rm A=\begin{bmatrix} 1 & a \\ 0 & 1 \end{bmatrix}$ where a ∈ ℕ, then is A¹⁰⁰ - A⁵⁰ - 2A²⁵ equal to?

where I is the identity matrix.

What is $\rm \sum\limits_{n=1}^{8n+7} i^n$ equal to, where i = √-1?