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

#2.2sum_(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# 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 #