Observe the following pattern:13 = 113 + 23 = (1 + 2)213 + 23 + 3

1.	Observe the following pattern:13 = 113 + 23 = (1 + 2)213 + 23 + 33 = (1 + 2 + 3)2Write the next three rows and calculate the value of 13 + 23 + 32 +.........+93 + 103 by the above pattern.
Answer» According to given pattern, = 1³ + 2³ + 3² + ......+n³) = (1 + 2 + 3 + ......+ n)² Here n = 10, so, = (1³ + 2³ + 3² + .....+ 9³ + 10³) = (1 + 2 + 3 +.......+9 + 10)² = (1³ + 2³ + 3³ +......+ 9³ + 10³) = (55²) = 55x55 = 3025.

Observe the following pattern:13 = 113 + 23 = (1 + 2)213 + 23 + 33 = (1 + 2 + 3)2Write the next three rows and calculate the value of 13 + 23 + 32 +.........+93 + 103 by the above pattern.

Answer»

According to given pattern,

= 1³ + 2³ + 3² + ......+n³) = (1 + 2 + 3 + ......+ n)²

Here n = 10, so,

= (1³ + 2³ + 3² + .....+ 9³ + 10³) = (1 + 2 + 3 +.......+9 + 10)²

= (1³ + 2³ + 3³ +......+ 9³ + 10³) = (55²) = 55x55 = 3025.