Calculus
Sequences and Series
Evaluate \[1 + 2 + 3 + \cdots + 98 + 99 + 100 = \sum_{i=1}^{100} i. \]
Let \[ S_n = \sum_{k=1}^{n} k^2.\]
Which of the following is not equal to \(S_6\)?
These numbers are called centered pentagonal numbers. A finite series can be used to find the answer.
Let \(\displaystyle S_n = \sum_{k=1}^{n} (-1)^{k^2 + k}\). Then \(S_n = \,\)?
Iterative Step: Walk halfway to B; this point is the starting point for the next iteration.
How many kilometers will Zeno have walked after performing the iterative step 100 times?