Q. 28 - Calculus

Question

Write each of the sums in Exercises 28 in sigma notation. Identify $m$ , $n$, and $a_k$ in each problem.

$-2^n-1^n+0^n+1^n+\cdots +n^n$

Step-by-Step Solution

Answer

Here, $m=-2,n=n$ and $a_k=k^n$

$\sum _{k=-2}^n{k}^n$

Step 1: Given information

The given series is $-2^n-1^n+0^n+1^n+\cdots +n^n$.

Step 2: Write the series in term of summation

Rewrite the given series in term of summation.

$-2^n-1^n+0^n+1^n+\cdots +n^n=\sum _{k=-2}^n{k}^n$

Step 3: Write the conclusion

The summation is $\sum _{k=-2}^n{k}^n$.