example 4 write series using summation notation write the series using summation notation. a. 25 +...
TRANSCRIPT
EXAMPLE 4 Write series using summation notation
Write the series using summation notation.
a. 25 + 50 + 75 + . . . + 250 34
23
12
45
b. + + + . . .
SOLUTION
Notice that the first term is 25(1), the second is 25(2), the third is 25(3), and the last is 25(10). So, the terms of the series can be written as:
a.
ai = 25i where i = 1, 2, 3, . . . , 10
The lower limit of summation is 1 and the upper limit of summation is 10.
EXAMPLE 4 Write series using summation notation
ANSWER
The summation notation for the series is10
i = 1
25i.
EXAMPLE 4 Write series using summation notation
Notice that for each term the denominator of the fraction is 1 more than the numerator. So, the terms of the series can be written as:
b.
ai = i + 1i where i = 1, 2, 3, 4, . . .
The lower limit of summation is 1 and the upper limit of summation is infinity.
ANSWER
The summation notation for the series is
8
i = 1 i + 1i .
GUIDED PRACTICE for Example 4
Write the series using summation notation.
6. 5 + 10 + 15 + . . . + 100
ANSWER20
i = 1
5i
7. 105 17+ + + + . . .941
216
ANSWER∞
i = 1 i2 + 1i2
GUIDED PRACTICE for Example 4
Write the series using summation notation.
ANSWER∞
i = 1
6i
8. 6 + 36 + 216 +1296 +. . .
ANSWER8
i = 1
4+ i
9. 5+ 6 + 7 +. . . 12