Observe the following pattern:13 = 113 + 23 = (1+2)213 + 23 + 33 = (1+

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 + 33 +…+ 93 by the above pattern.
Answer» According to given pattern, 1³ + 2³ + 3³ +…+ 9³ 1³ + 2³ + 3³ +…+ n³ = (1+2+3+…+n)² So when n = 10 1³ + 2³ + 3³ +…+ 9³ + 10³ = (1+2+3+…+10)² = (55)² = 55×55 = 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 + 33 +…+ 93 by the above pattern.

Answer»

According to given pattern,

1³ + 2³ + 3³ +…+ 9³

1³ + 2³ + 3³ +…+ n³ = (1+2+3+…+n)²

So when n = 10

1³ + 2³ + 3³ +…+ 9³ + 10³ = (1+2+3+…+10)²

= (55)²

= 55×55

= 3025