geometric series?! MATH!?
2017-10-22 11:02 pm
Find the value of x if the sum of the infinite geometric series 2x +4x^2 +8x^3+ .... is 5.
回答 (2)
2017-10-22 11:08 pm
✔ 最佳答案
Geometric series : 2x + 4x² + 8x³ + ……First term, T(1) = a = 2x
Common ratio = 4x²/(2x) = 8x³/(4x²) = 2x < 1
Sum to infinite term = 5
a / (1 - r) = 5
2x / [1 - (2x)] = 5
2x = 5 - 10x
12x = 5
x = 5/12
2017-10-22 11:36 pm
S=2x +4x^2 +8x^3+.......=5
S= 2x+(2x)²+(2x)³+......
Hence common ratio r= 2x and
S=(2x)/(1−r) =1/(1−(2x)) =5
i.e. 2x=5(1−(2x))
Hence 2x= 5−10x
i.e. 12x =5
i.e. x=5/12
S= 2x+(2x)²+(2x)³+......
Hence common ratio r= 2x and
S=(2x)/(1−r) =1/(1−(2x)) =5
i.e. 2x=5(1−(2x))
Hence 2x= 5−10x
i.e. 12x =5
i.e. x=5/12
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