Stepfan Ng, Tutor at University of California, Irvine Learning and Academic Resource Center (LARC) Calculus 2 Tutorial Leader, Numerade Educator

02:21

Precalculus with Limits

Pattern Recognition
$$
\begin{array} { l } { \text { (a) Compute the following sums of consecutive positive } } \\ { \text { odd integers. } } \\ { 1 + 3 = } \\ { 1 + 3 + 5 = } \\ { 1 + 3 + 5 + 7 = } \\ { 1 + 3 + 5 + 7 + 9 = } \\ { 1 + 3 + 5 + 7 + 9 + 11 = } \end{array}
$$$$
\begin{array} { l } { \text { (b) Use the sums in part (a) to make a conjecture about } } \\ { \text { the sums of consecutive positive odd integers. } } \\ { \text { Check your conjecture for the sum } } \\ { 1 + 3 + 5 + 7 + 9 + 11 + 13 = } \end{array}
$$(c) Verify your conjecture algebraically.

Chapter 9: Sequences, Series, and Probability

Section 2: Arithmetic Sequences and Partial Sums