Math11 Precalculus Q1 Week 9 ABC Key PDF

EXERCISES Pre- Expand the summation, and find the sum of the following:...

EXERCISES Pre- Expand the summation, and find the sum of the following: Calculus Quarter 1 Week 9—A (STEM _PC11SMI-Ii-1) ENRICHMENT ACTIVITY The learner applies the use of sigma notation in finding sums A. Apply the definition of sigma notation to find the sum. B. Answer the worked example online: Go to https://www.khanacademy.org/math/algebra-home/alg-series-and-induction/alg-sigma- notation/e/evaluating-basic-sigma-notation?modal=1  GENERALIZATION EXAMPLE 2 Expand the summation and find the sum: Mathematicians use the sigma notation to denote a sum. The upper- SOLUTION: case Greek letter Σ (sigma) is used to indicate a “sum”. The notation con- sists of several components or parts. Let f(i) be an expression involving an integer i The expression Can be compactly written in sigma notation, and we write it as EXAMPLE 3 Which is read “the summation of f(i) from i=m to n.” Here, m and n are Expand the summation and find the sum: integers with ,f(i) is a term (or summand) of the summation, and the letter i is the index, m is the lower bound and n is the upper bound. SOLUTION: EXAMPLE 1 EXAMPLE 4 Expand the summation and find the sum: Expand the summation and find the sum: SOLUTION SOLUTION: EXAMPLE 3 Evaluate Pre- Calculus SOLUTION 1 SOLUTION 2 EXAMPLE 4 EXERCISES Quarter 1 Week 9—A (STEM _PC11SMI-Ii-1) Evaluate each sum. The learner applies the use of sigma notation in finding sums. ENRICHMENT ACTIVITY Answer: Go to https://youtu.be/XJkIaw2e1Pw for more examples and discussion and to https://youtu.be/rf8Rd2Ar_aE for the proof Go to https://www.khanacademy.org/math/precalculus/x9e81a4f98389efdf:arith-series for the proof.  GENERALIZATION 2. The formula for the sum of Proof: in terms of n can be evaluated in different ways. A simple approach is Substitute the value of m=1 pictorial. number of terms EXAMPLE 1 Evaluate SOLUTION 1 SOLUTION 2 Using arithmetic series formula Another way is to use the formula for an arithmetic series with a1=1 and an=n: We have some useful summation facts based on the axioms of arithmetic addition and multiplication. 1. c is any real number EXAMPLE 2 Evaluate Proof: SOLUTION SOLUTION: Expand the function Pre- Calculus Separate each function and distribute the summation Apply the properties of summation Determine the formula to be used. Substitute the values in the formula. Quarter 1 Week 9 - C (STEM _PC11SMI-Ii-1) The learner applies the use of sigma notation in finding sums. EXERCISES Evaluate the following sums: ENRICHMENT ACTIVITY Evaluate the following sums: Go to https://youtu.be/Q6MBAvGyiEk for example and more clarification. Go to https://youtu.be/TeF09H13qyI for the proof and to https://youtu.be/U7nejGpTAP4 for the hint.  GENERALIZATION SOLUTION: Separate the two functions and distribute the summation We have some useful summation facts based on the axioms of arithmetic addition and multiplication. Apply the properties of summation 3. Determine the formula to be used. Substitute the values in the formula. Proof: EXAMPLE 2 Use the properties of sigma notation to evaluate the summation. SOLUTION 4. EXAMPLE 1 Use the properties of sigma notation to evaluate the summation. EXAMPLE 3 Use the properties of sigma notation to evaluate the summation.  ANSWER KEY Quarter 1 Week 9 – A Quarter 1 Week 9 – B Exercises Exercises Expand the summation, and find the sum of the following: A. Evaluate the sum 1. 60 1. 465 2. 70 2. 7260 3. 24 3. 325 4. 94 4. 1275 5. 340 5. 29240 6. 91 6. 50820 7. 540 7. 8. 450 8. Enrichment Activity 1. 465 Enrichment Activity Quarter 1 Week 9 – C Apply the definition of sigma notation to find the sum. 1. 70 Exercises 2. - 33 3. Evaluate the following sums: 1. 19900 2. - 20340 3. 5535700 4. 56925 Enrichment Activity Evaluate the following sums: 1. 183600 2. 664050 3. 25