Answer:
Solution given:
1:
-1/8=
2. -64/27
=
Express in rational number
1. (-3/2)=-3/2*2/2=-(3*2)*(2/2)=-6/4
2. (1/5)=1/5*5/5=<u>5/25</u>
and
(-4/3)³(2/5)-⁴ ÷ (7/4)
(-4³/3³)(2-⁴/5-⁴)÷7/4
(-64/27)(5⁴/2⁴)÷7/4
(-64/27)(625/16)÷7/4
(-64*625/(27*16))*4/7
-2500/27*4/7
-10000/169
(-100/13)²
A. Sigma notation
The formula for finding the nth value of the geometric series is given as:
an = a1 * r^n
Where,
an = nth value of the series
<span>a1 = 1st value in the geometric series = 940</span>
r = common ratio = 1/5
n = nth order
The sigma notation for the sum of this infinite geometric series is therefore,
(see attached photo)
B. Sum of the infinite geometric series
The formula for calculating the sum of an infinite geometric series is given as:
<span>S = a1 / (1 – r)</span>
Substituting the given values:
S = 940 / (1 – 1/5)
<span>S = 1,175</span>
