HOMEWORK \begin{tabular}{|l|l}\hline 1 & Write in Sigma notation. \ (a) $$ 1+2+3+4+5+6 $$ \ (b) $$ 1+4+9+16+25+36+49 $$\end{tabular}

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To express the given sums in Sigma notation, we will follow these steps:

### (a) $$ 1 + 2 + 3 + 4 + 5 + 6 $$

1. **Identify the pattern**: The series consists of the first 6 positive integers.
2. **Define the variable**: Let $$ n $$ be the index of summation.
3. **Determine the limits**: The sum starts from $$ n = 1 $$ and goes to $$ n = 6 $$.
4. **Write in Sigma notation**:

$$
\sum_{n=1}^{6} n
$$

### (b) $$ 1 + 4 + 9 + 16 + 25 + 36 + 49 $$

1. **Identify the pattern**: The series consists of the squares of the first 7 positive integers.
2. **Define the variable**: Let $$ n $$ be the index of summation.
3. **Determine the limits**: The sum starts from $$ n = 1 $$ and goes to $$ n = 7 $$.
4. **Write in Sigma notation**:

$$
\sum_{n=1}^{7} n^2
$$

### Final Answers

- (a) $$ \sum_{n=1}^{6} n $$
- (b) $$ \sum_{n=1}^{7} n^2 $$
(a) $$ \sum_{n=1}^{6} n $$ (b) $$ \sum_{n=1}^{7} n^2 $$

HOMEWORK \begin{tabular}{|l|l}\hline 1 & Write in Sigma notation. \\ (a) \( 1+2+3+4+5+6 \) \\ (b) \( 1+4+9+16+25+36+49 \)\end{tabular}

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