11. There is a group of 59 people who are patriotic out of which 30 believe in non-violence and rest 29 belien
in violence. Find the value of 30^3- 29^3using the pattern, (n + 1)^3 - n^3 = 1+3+ (n +1) *n
Answers
Given : There is a group of 59 people who are patriotic out of which 30 believe in non-violence and rest 29 believe
in violence.
To Find : the value of 30³- 29³ using the pattern, (n + 1)^3 - n^3 = 1+3 (n +1) *n
Step-by-step explanation:
(n + 1)^3 - n^3 = 1+3 (n +1) *n
first verification of the formula
a³ - b³ = (a - b)(a² + b² + ab)
( n + 1)³ - n³ = ( n + 1 - n) ( (n + 1)² + n² + n(n + 1))
= 1 ( n² + 2n + 1 + n² + n² + n)
= ( 3n² + 3n + 1)
= 3n (n + 1) + 1
= 1 + 3n(n + 1)
( n + 1)³ - n³ = 1 + 3n(n + 1)
n + 1 = 30
n = 29
30³ - 29³ = 1 + 3(29) (29 + 1)
= 1 + 87 ( 30)
= 1 + 2610
= 2611
30³ - 29³ = 2611
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