The following proof of the geometric series partial sum formula uses only sigma notation and simultaneous equations (many use the difference of two Geometric series: formula for the nth powers which is not studied in Mathematics (2U)) term and the sum of n terms. . The limiting sum formula should be derived from the partial geometric sum formula and the knowledge of limits approaching zero. The case ofshould be discussed using the word convergent to show it – converges on a single number. Limiting sum of geometric series The specific case of changing recurring decimals to fractions should be when explored here, however students should decide whether the limiting sum formula method or the simultaneous method is the best for them. The 2 other cases ofand should be discussed with the word divergent being used for that type of series. The use of spreadsheets designed to show how the balance decreases There are only a few variants of this type of question that depending on the interest, repayment amount or repayment time will give have been asked in previous HSC and the questions are students confidence in estimation of time frames. Bank simulations can be often of a high mark value. Recent examples of these found at or questions are: Q16b Applications to annuities and Q13d repayments. Q15c Common problems from the Marker’s notes include: incorrect number of instalments e.g. 2 (years) instead of 24 (months), rounding too soon, and using incorrect starting balance.
Geometric series: formula for the nth term and the sum of n terms. The following proof of the geometric series partial sum formula uses only sigma notation and simultaneous equations (many use the difference of two powers which is not studied in Mathematics (2U)) . Limiting sum of geometric series when The limiting sum formula should be derived from the partial geometric sum formula and the knowledge of limits approaching zero. The case ofshould be discussed using the word convergent – to show it converges on a single number. The specific case of changing recurring decimals to fractions should be explored here, however students should decide whether the limiting sum formula method or the simultaneous method is the best for them. The 2 other cases ofand should be discussed with the word divergent being used for that type of series. Applications to annuities and repayments. The use of spreadsheets designed to show how the balance decreases depending on the interest, repayment amount or repayment time will give students confidence in estimation of time frames. Bank simulations can be found at or There are only a few variants of this type of question that have been asked in previous HSC and the questions are often of a high mark value. Recent examples of these questions are: Q16b Q13d Q15c Common problems from the Marker’s notes include: incorrect number of instalments e.g. 2 (years) instead of 24 (months), rounding too soon, and using incorrect starting balance.
Series%20and%20series%20applications.docx