# In the following exercises Write the series using summation notation ?

## 4+7+12+19+... -3+4-5+6-7 1/3+1/9+1/27+1/81+....

Apr 19, 2018

$4 + 7 + 12 + 19. . . = {\sum}_{k = 1}^{n} {k}^{2} + 3$

$- 3 + 4 - 5 + 6 - 7. . . = {\sum}_{k = 1}^{n} {\left(- 1\right)}^{k} \left(k + 2\right)$

$\frac{1}{3} + \frac{1}{9} + \frac{1}{27} + \frac{1}{81.} . . = {\sum}_{k = 1}^{n} \frac{1}{{3}^{k}}$

where $n$ = the number of terms in the series.

#### Explanation:

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$4 + 7 + 12 + 19. . . = {\sum}_{k = 1}^{n} {k}^{2} + 3$

$- 3 + 4 - 5 + 6 - 7. . . = {\sum}_{k = 1}^{n} {\left(- 1\right)}^{k} \left(k + 2\right)$

$\frac{1}{3} + \frac{1}{9} + \frac{1}{27} + \frac{1}{81.} . . = {\sum}_{k = 1}^{n} \frac{1}{{3}^{k}}$

where $n$ = the number of terms in the series.