# Infinite Summation Internal Assessment The idea of this internal assessment is to investigate the effect changing the value of x and a have on the graph of the general sequence given.

Shin Park

January 20, 2011

Lancaster 3rd

Infinite Summation Internal Assessment

The idea of this internal assessment is to investigate the effect changing the value of x and a have on the graph of the general sequence given. In able to observe and display the following graph and tables, Microsoft Excel took action during this investigation. It is also vital to take note of the scatter plot lines with connected dots of the values of  at the different values of  is used for visual assistance to help understand the affect  and. The notation of  is the sum of the terms and  is the number of the term in the sequence.

The sequence that will be examine to determine the effect of different values of x and a is

=1, =, = , =  …, =  …

The first variation of the sequence that will be observed is, 1,,, with x = 1 and a = 2.

=

The table shows the value of, which is sum of the terms in the sequence, which gradually increase to 2, but never passes 2 regardless of the value of n increasing.

The graph above displays x=1 a=2 in the sequence and how its sum affects this line.  which is the x-axis, shows that  never passing through 2 because 2 is the horizontal asymptote, thus even if the value of n increases,  would still be smaller than 2.

The next sequence will be a similar concept of the previous one, but the change in values of x=1 and a=3 which is 1, , ,

=

This table show the value of , which is the sum of the sequence and never exceeds 3. This may be similar to the previous sequence but it varies as the  increase faster throughout the same value of  as  reaches to 3.

This graph displays x=1 and a=3,  on the value of. 3, which is the horizontal asymptote.

After the value of the x has been kept as 1 from the previous two graphs and tables, it is necessary to change the value of a and observe the affect on the sum of the sequence. Thus, same format of the sequence will be used with changing the value of a

1, , ,

=1 and =1

=

This table shows the same result of  throughout the increasing value of n which is 1. Therefore, with the table that is consistent, it can be assumed that the line of  will be a straight line, with no changing values.

This graph displays the value of =1 and =1 and .  Since the value of is 1 there is no change in the graph because the graph starts at 1 on the y-axis ...