find the sum of the following series:

(a+b)+(a^2+ab+b^2)+(a^3+a^2b+ab^2+b^3)+........

Question

find the sum of the following series: (a+b)+(a^2+ab+b^2)+(a^3+a^2b+ab^2+b^3)+........

Swapnil Saxena · Answer

The answer for the question is (For all a,b elonging to real no except 1 ) where n is the no of terms in the series.

Ashwin Muralidharan IIT Madras · Answer

Hi Satyaram,

Just multiply and divide the expression by (a-b) and sum it.

The expression will become

S = [(a²-b²) + (a³-b³) + (a⁴-b⁴) +..........]/(a-b)

So S = [ (a²+a³+....) - (b²+b³+.....) ] / (a-b)

So S = [ a²/(1-a) - b²/(1-b) ] / (a-b)

or S = (a+b-ab)/[(1-a)(1-b)]

Hope it helps.

Regards,

Ashwin (IIT Madras).

Sathya · Answer

How , So S = [ (a2+a3+....) - (b2+b3+.....) ] / (a-b) Became, So S = [ a2/(1-a) - b2/(1-b) ] / (a-b) ? Pls explain...And thnks for ur answer

Ashwin Muralidharan IIT Madras · Answer

Dude, Sum of infinite GP 1+a+a 2 +a 3 +...... = 1/(1-a) ----------- (Remember the Geometric Progressions formula) So a 2 +a 3 +a 4 +.... = a 2 /(1-a). Regards, Ashwin (IIT Madras).

Sathya · Answer

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find the sum of the following series: (a+b)+(a^2+ab+b^2)+(a^3+a^2b+ab^2+b^3)+........

find the sum of the following series:

(a+b)+(a^2+ab+b^2)+(a^3+a^2b+ab^2+b^3)+........

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