How do I use summation notation to write the series 2.2 + 6.6?

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Answer 1 · 2016-08-11T14:59:08

$2.2 \sum i = 0 \to n - 1 3^{i}$ $2.2sum_(i=0ton-1)3^i$

Just two terms is not really enough to build the series with confidence. However, lets build based on an assumption:

Let each term be represented by $a_{i}$ $a_i$ where $i=1,2,3,4...n$

Let
$a_i->a_1=2.2$
$a_i->a_2=6.6$
$a_i->a_3=19.8$
$a_i->a_4=59.4$
and so on.

Let the sum be $s$
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Notice that
$a_2=3a_1$
$a_3=3a_2 = 3xx3a_1$
$a_4=3a_3=3xx3xx3a_1$

Notice that we have $a_i=3^(i-1)(2.2)$

Test: $a_1=3^(1-1)(2.2) = 3^0(2.2) = 1(2.2)=2.2$

$s=a_1+a_2+a_3+...+a_n$

$s=3^0(2.2)+3^1(2.2)+...+3^(i-1)(2.2)+...+3^(n-1)(2.2)$

Factor out the 2.2 giving:

$2.2(3^0+3^1+3^2+...+3^(i-1)+...3^(n-1))$

So the notation is

$2.2sum_(i=0ton-1)3^i$