# IB Math HL Portfolio Type I Series and Induction

Mathematics Higher Level Portfolio Type I Series and Induction

Acknowledgement

Question sheet should directly be given from your IB Mathematics HL teachers. This is due to the fact that IB students are not allowed to hold any question paper; every candidate must finish this coursework and return the question sheet in five days. Therefore I was not able to include any questions in this portfolio.

Introduction

This Investigation of the Series and Induction Portfolio for Math HL brings out that the sum of terms of series following a certain pattern can be predicted as expressions by studying these patterns. With the resourceful use of a calculator, studying the graphs and undertaking regression of the data we can easily deduce the general term and by further considering similar series we can predict they're expressions which emerge rational and true when induced in terms of a proposition. Recalling that 1+2+3+4+5+........+. 1. Considering where is the general term and 'n' is the number of terms, Let us take into consideration the first term, The first term implies that . Since = 1, We can also say that, Let us also take into consideration, The second term implies that  and so on.

Question 1

a1 = 1∙2 = 2

a2 = 2∙3 = 6

a3 = 3∙4 = 12

a4 = 4∙5 = 20

a5 = 5∙6 = 30

a6 = 6∙7 = 42

an = n(n+1) = n2+n

Question 2

A)

S1 = a1 = 2

S2 = a1+ a2 =8

S3 = a1++ a3 = 20

S4 = a1++ a4 = 40

S5 = a1++ a5 = 70

S6 = a1++ a6 = 112

Sk = a1++ ak

B) Sn =

=

=

=

=

∴ Sn =

C)  1∙2+2∙3+3∙4++n(n+1) =

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