Calculus

Sequences and Series

Finite Series

         

Evaluate 1+2+3++98+99+100=i=1100i.1 + 2 + 3 + \cdots + 98 + 99 + 100 = \sum_{i=1}^{100} i.

Let Sn=k=1nk2. S_n = \sum_{k=1}^{n} k^2.

Which of the following is not equal to S6S_6?

These numbers are called centered pentagonal numbers. A finite series can be used to find the answer. These numbers are called centered pentagonal numbers. A finite series can be used to find the answer.

Let Sn=k=1n(1)k2+k\displaystyle S_n = \sum_{k=1}^{n} (-1)^{k^2 + k}. Then Sn=S_n = \,?

The distance from A to B is 10 kilometers. Starting at A, Zeno repeats the following step:

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?

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