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a^(2)+ab(b+1)+b^(3)...

a^(2)+ab(b+1)+b^(3)

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If a = (sqrt5 + 1)/(sqrt5 + 1) and b = (sqrt5 -1)/(sqrt5 + 1) , then find the value of (a) (a^(2) + ab + b^(2))/(a^(2) - ab + b^(2)) (b) ((a -b)^(3))/((a + b)^(3)) (c) (3a^(2) + 5ab + b^(2))/(3a^(2) - 5ab + b^(2)) (d) (a^(3) + b^(3))/(a^(3) - b^(3))

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 .

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 .

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 .

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 .

Show that |{:(1+a^(2)-b^(2),,2ab,,-2b),(2ab,,1-a^(2)+b^(2),,2a),(2b,,-2a,,1-a^(2)-b^(2)):}| = (1+a^(2) +b^(2))^(3)

Show that |{:(1+a^(2)-b^(2),,2ab,,-2b),(2ab,,1-a^(2)+b^(2),,2a),(2b,,-2a,,1-a^(2)-b^(2)):}| = (1+a^(2) +b^(2))^(3)

If |a| lt 1, |b| lt 1 , then show that a(a+b) + a^(2) (a^(2) + b^(2)) + a^(3)(a^(3) + b^(3)) +… = (a^(2))/(1-a^(2)) + (ab)/(1- ab)

a^(3)+3a^(2)b+3ab^(2)+b^(3) divided by a^(2)+2ab+b^(2) is