b) $$ \sum_{n=0}^{5}(-2 n)^{n+1} $$

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Calculate or simplify the expression $$ \sum_{n=0}^{5}(-2n)^{n+1} $$.
Find the sum by following steps:
- step0: Solution:
  $$\sum _{n=0}^{5}\left(-2night)^{n+1}$$
- step1: Convert the expressions:
  $$\left(-2	imes 0ight)^{0+1}+\left(-2	imes 1ight)^{1+1}+\left(-2	imes 2ight)^{2+1}+\left(-2	imes 3ight)^{3+1}+\left(-2	imes 4ight)^{4+1}+\left(-2	imes 5ight)^{5+1}$$
- step2: Calculate:
  $$0+4-64+1296-32768+10^{6}$$
- step3: Calculate:
  $$-31532+10^{6}$$
The sum of the series $$ \sum_{n=0}^{5}(-2n)^{n+1} $$ is $$ 968468 $$.
The sum of the series $$ \sum_{n=0}^{5}(-2n)^{n+1} $$ is 968468.

b)

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