Chapter B, Problem 31AYU

To determine

To find: The first five terms in the sequence of partial sums for each series.

Answer to Problem 31AYU

Solution:

The first five terms in the sequence of partial sums for each series is $1, 3, 6, 10, 15$.

Explanation of Solution

Given:

${\displaystyle {\sum }_{k = 1}^{\infty }k}$

Calculation:

${\displaystyle \sum _{k = 1}^{\infty }k = 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 + \cdots \mathrm{....}}$

The first five terms in the sequence of partial sums for each series is

$\begin{array}{l}1\\ 1 + 2 = 3\\ 1 + 2 + 3 = 6\\ 1 + 2 + 3 + 4 = 10\\ 1 + 2 + 3 + 4 + 5 = 15\end{array}$

The first five terms in the sequence of partial sums for each series is $1, 3, 6, 10, 15$.