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The sum of a sequence (Posted on 2004-12-14)

Find the sum of the sequence: x, 2x², 3x³, 4x⁴, 5x⁵, ... , nxⁿ.

See The Solution Submitted by Mohammad

Rating: 3.4286 (7 votes)

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calculus solution

| Comment 1 of 10

Let f(x)= 1+x+...+x^n=(x^(n+1)-1)/(x-1). Then the sum sought is xf'(x)=x(nx^(n+1)-(n+1)x^n+1)/(x-1)^2. For example, 2+2*2^2+3*2^3+4*2^4=2+8+24+64+98 while 2*(4*2^5-5*2^4+1)/1=2*(128-80+1)=2*49=98.

Posted by Richard on 2004-12-14 17:41:22

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