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1.5+2.5²+3.5²+..........................+n.5^n equals

1.5+2.5²+3.5²+..........................+n.5^n equals

Grade:11

2 Answers

Arun
25763 Points
2 years ago
Dear student
 
is the third term is 3. 5^3 or 3.5^2
 
Please check and repost this. you can also attach an image.
 
I will be happy to help you.
 
Regards
Arun (askIITians forum expert)
Aditya Gupta
2075 Points
2 years ago
the above is simply the example of a AGP (Arithmetic-Geometric Progression)
using geometric series sum formula we have
1+x+x^2+x^3+....+x^n= (x^(n+1) – 1)/(x – 1)
differntiate wrt x 
1+2x+3x^2+...+nx^(n-1) = [x^n(nx-n-1)+1]/(x-1)^2
 multiply by x both sides and substitute x=5
x+2x^2+3x^3+...+nx^n at x=5 = 5[5^n(4n-1)+1]/16

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