ben3898
17.08.2020 •
Mathematics
What is the sum to 'n' terms of the series √5,√20,√45,√80,?
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Ответ:
Sₙ = √5/2 n (n + 1)
Step-by-step explanation:
Given AP:
√5,√20,√45,√80,...Rewriting as:
√5,√4*5,√9*5,√16*5,...√5, 2√5, 3√5, 4√5,..., n√5Common difference:
d= 2√5 - √5 = √5Sum of n terms:
Sₙ = 1/2n (a₁ + aₙ) =1/2n (√5 + √5 + (n-1)√5) =1/2n (n + 1)√5=√5/2 n (n + 1)Sₙ = √5/2 n (n + 1)
Ответ: