1. Write the following in expanded for then find the sum
a) ^7(Sigma sign) k=0 (k=1)(k+2)
b) ^7(Sigma sign) k=4 3k
Note: The sigma sign does not show up when pasted here. The 7 is on top of the sigma sign and the k= 0 or k=2, respectively, lies below the sigma sign.

2. Express the following series using sigma notation:
a) (1 X 0)/2 + (2 X 1)/3 + (3 X 2)/4 + ........ (10 X 9)/11
b) (1 X 2)/2 + (2 X 3)/4 + (3 X 4)/6 + .......... (8 X 9)/16

3. Use the Binomial Theorem to expand the following equation:
a) (2p - 3q)^4
b) (2p + 1)^4

4. Find the fifth term in the expansion of (4x + 2y)^7

5. Find the sum of the following series, or state that the sum does not exist
a) 12 + 8 + 16/3 + .......
b) 1/12 + 1/2 + 3 + .........

6. Find the limit of the following or state that the limit does not exist
a) (2n - 1)/n^3
b) ......as n approches infinity of (2n^2)/(n^2 - 1)

Solution Preview

1. ∑_(k=0)^7▒(k+1)(k+2)
First, since this is summation from k=0 to k=7,
We could transform the expression into the following:
∑_(k=0)^7▒(k+1)(k+2) =(0+1)*(0+2)+(1+1)*(1+2)+(2+1)*(2+2)+(3+1)*(3+2)+(4+1)*(4+2)+(5+1)*(5+2)+(6+1)*(6+2)+(7+1)*(7+2)=1*2+2*3+3*4+4*5+5*6+6*7+7*8+8*9=240

2. ∑_(k=4)^7▒〖3k=3*4+3*5+3*6+3*7=66〗

3. a)(1*0)/2+(2*1)/3+(3*2)/4+⋯+(10*9)/11
First, in the first value, for the two numbers in the numerators, they are 1 and 2 less than denominator respectively.
Therefore, if k starts from 0, the first number a0=(0+1)*0/(0+2) or (k+1)k/(k+2) in general. ...

... and Geometric Sequences, Series and Functions. Using the index of a sequence as the domain and the value of the sequence as the range, is a sequence a function? ...

Index of a Series, Functions, Arithmetic and Geomteric Sequences. ...series as the range, is a series a function... Which one of the basic functions (linear, quadratic ...

... independent variable and the value of the series as the ... It also includes real life applications of the sequences. Using the index of a sequence as the domain ...

... independent variable and the value of the series as the ... It also includes real life applications of the sequences. Using the index of a sequence as the domain ...

... independent variable and the value of the series as the ... It also includes real life applications of the sequences. Using the index of a sequence as the domain ...

...functions (linear, quadratic, rational, or exponential) is related to the geometric sequence? ... Give at least two real-life examples of a sequences or series. ...

...functions (linear, quadratic, rational, or exponential) is related to the geometric sequence? ... Give at least two real-life examples of a sequences or series. ...

... Give real-life examples of both arithmetic and geometric sequences and series. ... Yes, it is a function by using the index of a sequence as the domain and the ...

Examples of Arithmetic series and sequence. ... rational, or exponential) is related to the geometric series? ... of both arithmetic and geometric sequences and series. ...