Use Differentiation To Prove That1+2x+3x^2+4x^3+......till Infinity Is 1/(1-x)^2 for |x|
Shadic The Hedgehog , 4 Years ago
Grade 11
Differential Calculus> Use Differentiation To Prove That 1+2x+3x...
1 Answers
Aditya Gupta
Last Activity: 3 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.
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