Evaluate the follow (1) $$ \sum_{k=1}^{50}(3 k+1) $$ 4) $$ \sum_{r=2}^{7} \frac{30}{3^{r-3}} $$

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Calculate or simplify the expression $$ \sum_{k=1}^{50}(3k+1) $$.
Find the sum by following steps:
- step0: Solution:
  $$\sum _{k=1}^{50}\left(3k+1ight)$$
- step1: Calculate:
  $$\sum _{k=1}^{50}3k+\sum _{k=1}^{50}1$$
- step2: Calculate:
  $$3825+\sum _{k=1}^{50}1$$
- step3: Calculate:
  $$3825+50$$
- step4: Add the numbers:
  $$3875$$
Calculate or simplify the expression $$ \sum_{r=2}^{7} \frac{30}{3^{r-3}} $$.
Find the sum by following steps:
- step0: Solution:
  $$\sum _{r=2}^{7}\frac{30}{3^{r-3}}$$
- step1: Rewrite the expression:
  $$\sum _{r=2}^{7}\frac{30}{\frac{1}{27}	imes 3^{r}}$$
- step2: Rewrite the expression:
  $$\sum _{r=2}^{7}810	imes 3^{-r}$$
- step3: Convert the expressions:
  $$810	imes 3^{-2}+810	imes 3^{-3}+810	imes 3^{-4}+810	imes 3^{-5}+810	imes 3^{-6}+810	imes 3^{-7}$$
- step4: Calculate:
  $$90+30+10+\frac{10}{3}+\frac{10}{9}+\frac{10}{27}$$
- step5: Calculate:
  $$\frac{3640}{27}$$
The sum of the series $$ \sum_{k=1}^{50}(3k+1) $$ is 3875.

The sum of the series $$ \sum_{r=2}^{7} \frac{30}{3^{r-3}} $$ is $$ \frac{3640}{27} $$ or $$ 134\frac{22}{27} $$ or approximately 134.814.
The sum of $$ \sum_{k=1}^{50}(3k+1) $$ is 3875. The sum of $$ \sum_{r=2}^{7} \frac{30}{3^{r-3}} $$ is $$ \frac{3640}{27} $$ or approximately 134.814.

Evaluate the follow
(1)
4)

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