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Let $\text{S} =\displaystyle \sum_{i=1}^n f(x_i), \text{A}=\displaystyle\sum_{i=1}^{a} f(x_i)$ and $\text{B}=\displaystyle \sum_{i=a}^n f(x_i)$ then
Which of the following is/are true?

(Consider f as some arbitary function)

1. $\text{S = A + B}$
2. $\text{S}=\displaystyle \sum_{i=1}^{a-1} f(x_i)+f(a)+ \text{B}$
3. $\text{S}=\displaystyle \sum_{i=1}^{a-1} f(x_i)+f(a)+ \text{B}$
4. $\text{S = A + B}-f(a)$

Option B and C are same. Please correct it.
Option A,B,C same.
In option C, f(a) should not be there.

A is false because it is adding two times at $i=a.$

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Since option B & C are same. So, if option B is false then option C is also false.

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