Chapter 8, Problem 3CR

To determine

Find the series using summation notation.

Answer to Problem 3CR

The summation notation for the series is ${\displaystyle \sum _{i=0}^{\infty }i\left(i+1\right)}$ .

Explanation of Solution

Given:

The given series is $0+2+6+12+---$ .

Calculation:

Notice that the

First term $=$$0\cdot \left(0+1\right)=0$

Second term $=$$1\cdot \left(1+1\right)=2$

Third term $=$$2\cdot \left(2+1\right)=6$

Fourth term $=$$3\cdot \left(3+1\right)=12$

From the above pattern, the terms of the series can be written as

  $a_i=i\left(i+1\right),\text{where}i=0,1,2,3---\infty$

The lower limit of summation is $0$ and the upper limit of summation is $\infty$ .

Hence the summation notation for the series is ${\displaystyle \sum _{i=0}^{\infty }i\left(i+1\right)}$ .