0

Guest

Courses New

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
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.
KINDLY APPROVE :))

Think You Can Provide A Better Answer ?

Other Related Questions on Differential Calculus

View all Questions »

ASK QUESTION

Get your questions answered by the expert for free

Answer and earn gift vouchers

Win Gift vouchers upto Rs 500/-

View courses by askIITians

Design classes One-on-One in your own way with Top IITians/Medical Professionals

Click Here Know More

Complete Self Study Package designed by Industry Leading Experts

Click Here Know More

Live 1-1 coding classes to unleash the Creator in your Child

Click Here Know More

a Complete All-in-One Study package Fully Loaded inside a Tablet!

Click Here Know More