Sigma Notation

Source metadata

Repeated running header: 2025 TJC H2 Math (9758) JC2 MSM: SIGMA NOTATION. The first question and solution pages also carry the bold topic heading SIGMA NOTATION. Solution pages are numbered 1–10. Question printed pages are 102–104. Repeated “Solution” and “Answers” headings are represented by the corresponding native section headings.

Question index

• 14-01: An integer upper limit in an inequality
• 14-02: Sum a block of odd squares
• 14-03: A polynomial term and a middle block
• 14-04: Combine an alternating GP with logarithms
• 14-05: A trigonometric block sum
• 14-06: Telescoping logs and a rational GP ratio
• 14-07: An infinite tail from a supplied sum
• 14-08: A factorial tail after reindexing
• 14-09: An error bound and a shifted rational sum
• 14-10: Shift an exponential summation identity
• 14-11: A radical sum with one extra endpoint
• 14-12: Apply the absolute root test

Printed answer index

1. $\{a:a>3,a\in\mathbb Z^+\}$

2. (ii) $\frac{2m(16m^2-1)}3-286$

3. 574753

4. (i) $\frac16[1-(-1/2)^k]+\ln[(k+1)!]$; (ii) does not exist

5. $k=11/2$

6. (a) $S_N=\ln2-\ln[N(N+1)]$; (b)(i) $-0.25<x<0.5$; (b)(ii) 1.5

7. $1/160$

8. (a) $3/2$; (b) $1/20$

9. (i) 998; (ii) $1/19-1/(4n+1)$

10. $a=1/3,b=9/2$

11. No separate short-answer entry is printed for this question; the worked solution is retained above.

12. No separate short-answer entry is printed for this question; the worked solution is retained above.

Calculator display conventions

Repeated graph/table status strips show NORMAL FLOAT AUTO REAL RADIAN MP (as applicable), PRESS ↑ FOR ΔTbl, Plot1 Plot2 Plot3, Y1/Y2, and Intersection or Zero. These calculator display labels and the associated mathematical equations, root/intersection readouts, and table values are expressed in each question’s native sections. The controls explain the original calculator workflow; they are not interactive screenshots.