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MTH 1322 – Calculus II Homework 12 – Summing an Infinite Series 1. Write the series in Σ-notation and evaluate its sum. (c) 1 2 − 1 6 + 1 18 − 1 54 + 1 162 − 1 486 + · · · Hint : This is a geometric...

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MTH 1322 – Calculus II
Homework 12 – Summing an Infinite Series
1. Write the series in Σ-notation and evaluate its sum.
(c)
1
2
− 1
6
+
1
18
− 1
54
+
1
162
− 1
486
+ · · · Hint : This is a geometric series.
(d)
1
1 · 3
+
1
3 · 5
+
1
5 · 7
+
1
7 · 9
+
1
9 · 11
+ · · · Hint : This is a telescoping series.
2. Determine whether the series converges or diverges.
(d)
∞∑
n=2
1
n
√
3
4. Use a geometric series to show that 0.4999 . . . =
1
2
.
mth1322hw12-vbjglo3z.pdf
Answered Same Day Jun 23, 2021

Solution

Rajeswari answered on Jun 24 2021
149 Votes
Summing an infinite series
The sum can be written as
This is a geometric series with first term a= ½ and common ratio r=-1/3.
|r| = 1/3 <1
Using the formula, Sum =
We write general term as
, n is a natural numbe
We can decompose as partial fraction as
i.e. we have the terms
This is a...
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