Question

Enter the correct letter to match each summation expression with the property or formula. N Σ i=1 cai is equal to . A n(n + 1)(2n + 1) 6 n Σ i=1 i is equal to . B n(n + 1) 2 n Σ i=1 c is equal to . C c n Σ i=1 ai n Σ i=1 i3 is equal to . D cn n Σ i=1 i2 is equal to

Answer 1

c, b, d, e, a

Explanation:

Answer 2

Explanation:

1) The sum of a series of the cubes of numbers 'i' is given as follows;

Sₙ = n/2 × (1st term + Last term)

∴ Sₙ = n/2 × (1 + n) = n·(n + 1)/2

It can be shown that the sum of a series of the cubes of numbers 'i²' is given as follows;

Sₙ = (n·(n + 1)·(2·n + 1))/6

It can be also be shown that the sum of a series of the cubes of numbers 'i³' is given as follows;

Sₙ = (n·(n + 1)/2)²

Therefore, we have;

.