Test: Binomial Series - Ambitious

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Question 1:   Find the value of 16! 13!
3360
16 13
240
0
Question 2:   Find the value of 4! 0!
24
1
0
Does not exist
Question 3:   Knowing that combinational coefficient C r n = n! ( n-r )!r! , find C 1 5
5
1
0
25
Question 4:   Simplify: ( 3n )! ( 3n+2 )!
1 ( 3n+3 ) 2
3n 3n+2
1 ( 3n+2 )( 3n+1 )
1 ( 3n+3 )( 3n+2 )
Question 5:   Find the coefficient of x 4 in the binomial expansion of ( 2 3 x ) 9
1 x 4
353682 x 4
326592 x 4
647378 x 4
Question 6:   Find the 7 th term of ( 3 x 4 ) 13 in the binomial expansion
2 5 x 6
1 3 x 6
938223 x 6 1024
3 7 x 6
Question 7:   Write down the sum of the first n terms using sigma notation of the following series: 1+23+45+67+8...
n=1 n ( 1 ) n n
n=1 n ( 1 ) n n
n=1 n n
n=1 n ( 1 )n
Question 8:   Find the value of n=1 70 n
2500
70
2485
140
Question 9:   Find the value of r=1 n ( 18r+3 )
9 n 2 +3
18 n 2 +4
3n(3 n 2 +4)
n(3 n 2 +3)
Question 10:   Knowing binomial expansion of e x find e 0.41 by calculating first 5 terms in the series
1.497722
1.5067144
1.603416
1.57568