Q5. How many terms does the sum of k for k = 4 to 9 have, and what is the sum?
9 − 4 + 1 = 6 terms: 4 + 5 + 6 + 7 + 8 + 9 = 39.
Q6. Write out and evaluate the sum of (−1)k+1k for k = 1 to 4.
k = 1, 2, 3, 4 give +1, −2, +3, −4: 1 − 2 + 3 − 4 = −2.
Q7. Write 1 × 2 + 2 × 3 + 3 × 4 + 4 × 5 in sigma notation and evaluate it.
The kth term is k(k + 1), so it is the sum of k(k + 1) for k = 1 to 4: 2 + 6 + 12 + 20 = 40.