Sum of the series when i and j are independent

Problems on Sum of the Series When I and J are Dependent

Find the Sum of sine series when angle are in AP

Find the Sum of Cosine series when angle are in AP

Find the sum of n terms of the series when nth terms is : (i)n^(2)+n" "(ii)n^(2)+2^(n)

Examine if vec(i) - 3vec(j) + 2vec(k), 2vec(i) - 4vec(j) - vec(k) and 3vec(i) + 2vec(j) - vec(k) are linearly independent or dependent .

Are the following set of vectors linearly independent? vec(a) = hat(i) - 2hat(j) + 3hat(k), vec(b) = 3hat(j) - 6hat(j) + 9hat(k)

The sum of an infinite geometric series is 2 and the sum of the geometric series made from the cubes of this infinite series is 24. Then the series is: