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Use Differentiation To Prove That 1+2x+3x^2+4x^3+......till Infinity Is 1/(1-x)^2 for |x|

Use Differentiation To Prove That
1+2x+3x^2+4x^3+......till Infinity Is 1/(1-x)^2 for |x|
 

Grade:11

1 Answers

Aditya Gupta
2081 Points
2 years ago
by sum of infinite GP we know that x+x^2+x^3+.....= x/(1 – x)= 1/(1 – x) – 1= (1 – x)^(-1) – 1
diff both sides, we get 
1+2x+3x^2+4x^3+......till Infinity= -1.(1 – x)^(-2).(-1)= 1/(1 – x)^2.
QED.
KINDLY APPROVE :))

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