Home
Class 12
MATHS
Find the sum of n terms of the series (a...

Find the sum of n terms of the series `(a+b)+(a^(2)+ab+b^(2))+(a^(3)+a^(2)b+ab^(2)+b^(3))+"......."` where `a ne 1,bne 1` and `a ne b`.

Text Solution

Verified by Experts

` a ne1 b ne 0 and ane b `
Let S = ( a+ b) + `(a^(2) + ab + b^(2)+ ( a^(3) + a^(2) b+ ab^(2) +b^(3) + ….+ n ` terms
`=(1) /( (a-b) ) [(a^(2)-b^(2)) + ( a^(3) -b ^(3)) + (a^(4) -b^(4) ) + ....+_n terms ]`
`= (1) /((a-b) ) [a^(2) (1+ a+ ......+ nterms )- b ^(2)(1+ b+ b^(2) + .....+n terms ) `

` =(1)/( (a- b) ) [ a^(2)* (1* (a^(n) -1) )/( (a-1) ) -b^(2) ( 1* (b^(n) -1))/( (b-1) ) ]`
` " " = (1)/( (a-b ) ) [a^(2) ((1- n^(2)))/( (1- a) ) - b^(2) ( ( 1- b^(n)))/( (1-b) ) ]`
Promotional Banner

Similar Questions

Explore conceptually related problems

(b)Find the sum of first n terns of the series 1^2+2^2+……+n^2 .

Find the sum to n terms of the series , (1)/(1.2)+(1)/(2.3)+(1)/(3.4)+.... ?

Sum to n terms of the series 1+(1+2)+(1+2+3)+.. ..

Sum of n terms of the series 1+2 x+3 x^(2)+4 x^(3)+..,(x ne 1) is

Factorise a ^(3) - 3a^(2) b + 3ab ^(2) -b ^(3)

Find the slope of bar(AB) , where A(2, 1), B(2, 6)

(b) Find the sum to n terms of the series 1 xx 2 xx 3 + 2 xx 3 xx 4 + 3 xx 4 xx 5 + .. .

Find the slope of bar(AB) , where A(-2, 8), B(-2, -2)

Find the slope of bar(AB) , where A(-4, 2), B(-4, -2)

The sum of first n terms of an AP is 3n^(2) + 4n . Find: a] a_(25) b] a_(10)