In arithmetic series SN is equal to k + 2 k + 3 k ...+ 100, k is a positive integer and k is a factor of 100 then Sn is equal to
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Answer:
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Step-by-step explanation:
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Given : Sₙ = k + 2 k + 3 k .......... + 100 and k is a factor of 100
To show : Sn = 50 + 5000/k
Solution:
Sₙ = k + 2 k + 3 k .......... + 100
Taking k as common
=> Sₙ = k(1 + 2 + 3 + .......... + 100/k)
n = 100/k
d = 1
=> Sₙ = k ( 100/2k) (1 + 100/k)
=> Sₙ = 50 ( 1 + 100/k)
=> Sₙ = 50 + 5000/k
=> Sₙ = 50 + 5000/k
Sₙ = 50 + 5000/k if Sₙ = k + 2 k + 3 k .......... + 100
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