If `a=-2`, then `a+a^(2)-a^(3)+a^(4)-a^(5)=`

Find the determinant of the matrix [(1^(2),2^(2),3^(2)),(2^(2),3^(2),4^(2)),(3^(2),4^(2),5^(2))]

If a^(*)b=a^(2)+b^(2), then the value of (4*5)*3 is a^(*)b=a^(2)+b^(2), then the value of (4*5)*3 is (4^(2)+5^(2))+3^(2)( ii )(4+5)^(2)+3^(2)41^(2)+3^(2)( iv) (4+5+3)^(2)

The value of the determinant |{:(1^(2),2^(2),3^(2),4^(2)),(2^(2),3^(2),4^(2),5^(2)),(3^(2),4^(2),5^(2),6^(2)),(4^(2),5^(2),6^(2),7^(2)):}| is

The value of |{:(2^(2),2^(3),2^(4)),(2^(3),2^(4),2^(5)),(2^(4),2^(5),2^(6)):}| is

The sum of the infinite series, 1 ^(2) -(2^(2))/(5) + (3 ^(2))/(5 ^(2))+ (4^(2))/(5 ^(3))+ (5 ^(2))/(5 ^(4))-(6 ^(2))/(5 ^(5)) + ..... is:

If a * b=a^2+b^2, then the value of (4 * 5) * 3 is (i) (4^2+5^2)+3^2 (ii) (4+5)^2+3^2 (iii) 41^2+3^2 (iv) (4+5+3)^2

If |{:(3^(2)+k,4^(2),3^(2)+3+k),(4^(2)+k,5^(2),4^(2)+4+k),(5^(2)+k,6^(2),5^(2)+5+k):}| =0, then sqrt(2^(k)sqrt(2^(k)sqrt(2^(k)cdotsoo))) is _____

If |{:(3^(2)+k,4^(2),3^(2)+3+k),(4^(2)+k,5^(2),4^(2)+4+k),(5^(2)+k,6^(2),5^(2)+5+k):}| =0, then sqrt(2^(k)sqrt(2^(k)sqrt(2^(k)cdotsoo))) is _____