Discrete Structure lecture_17

Apr 28th, 2015
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It includes all the details about the Discrete structure with examples.Step by step solution.

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DISCREAT STRUCTURELECTURE # 17ARITHMETIC SERIESKHAWAJA TARIQ MAHMOODLecture # 17SERIESSERIES:The sum of the terms of a sequence forms a series. If a1, a2, a3, represent a sequence ofnumbers, then the corresponding series isa1 a2 a3 ........... akk 1COMPUTING SUMMATIONS:EXAMPLE:Let a0 2, a1 3, a2 2, a3 1 and a4 0 Compute each of the summations:241.ai 0a2.ij 01j3.ak 1kSOLUTION:41.ai 0i a0 a1 a2 a3 a4 2 3 2 1 0 2 3 2 1 0422.aj 0j a0 a1 a2 2 3 2 2 3 2313.ak 1k a13EXAMPLE:3Compute the summations 2i 1i 1Khawaja Tariq Mahmood.Page 2Lecture # 17SERIESSOLUTION:3 2i 1 2 1 1 2 2 1 2 3 1i 1 2 1 4 1 6 1 1 3 59EXPANDED FORM TO SUMMATION NOTATION:EXAMPLE:Write the following using summation notation:123n 1 .......... n n 1 n 22nSOLUTION:We find the k th term of the series. The numerators forms an arithmetic sequence 1, 2,3,........, n 1in whichFirst term&a1 1Common difference d 2 1 1ak a1 k 1 d 1 k 11 1

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