IIT JEE , AIEEE Forum - Mathematics , Differential Calculus

goal10

Find the sum of , using calculas

pink_ele

consider sigma nx^n=S
S=x+2x^2+3x^3....................
Sx= x^2+2x^3.....................
S(1-x)=x+x^2+x^3...............
S=x(1-x^n)/(1-x)^2
diff dis wrtx...........to get d ans
i.e
={(1-x^2)(1-(n+1)x^n)+2x(1-x)(1-x^n)}/(1-x)^2
is it so!

goal10

ANSWER iS .

allamraju

First we find the sum of the following infinite A.G.P

Now,on differentiating on both sides,we have,

Sorry made a small mistake earlier and so edited it.

goal10

But allamraju answer is not matching.......

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First we find the sum of the following infinite A.G.P

Now,on differentiating on both sides,we have,

Sorry made a small mistake earlier and so edited it.