I=6^2+6^3+6^4....6^100 K=(-8)+(-8)^2+(-8)^3+.....+(-8)^19+(-8)^20

To find the values of I, K, A, B, and C, we can use the formulas for the sum of a geometric series.

For I, we have a geometric series with a common ratio of 6 and the first term being 6^2. The sum of this series is given by the formula:

I = (6^2 * (1 - 6^99)) / (1 - 6) = (36 * (1 - 6^99)) / (-5)

For K, we have a geometric series with a common ratio of -8 and the first term being -8. The sum of this series is given by the formula:

K = (-8 * (1 - (-8)^20)) / (1 - (-8)) = (-8 * (1 - 8^20)) / 9

For A, we have a geometric series with a common ratio of 2 and the first term being 2^3. The sum of this series is given by the formula:

A = (2^3 * (1 - 2^97)) / (1 - 2) = (8 * (1 - 2^97)) / (-1)

For B, we have a geometric series with a common ratio of 3 and the first term being 3^2. The sum of this series is given by the formula:

B = (3^2 * (1 - 3^99)) / (1 - 3) = (9 * (1 - 3^99)) / (-2)

For C, we have a geometric series with a common ratio of 4 and the first term being 4^0. The sum of this series is given by the formula:

C = (4^0 * (1 - 4^100)) / (1 - 4) = (1 * (1 - 4^100)) / (-3)

Now we can calculate the values of I, K, A, B, and C using these formulas.