Question

If 1"2+2"2+.....n"2/1+2....n=17 then the sum of
Summation k=1,upto n,(2k-1)
A)576
B)676
C)625
D)900

Answer 1

Option (C) 625 is correct

Step-by-step explanation:

Given,

(1² + 2² + ... + n²) / (1 + 2 + ... + n) = 17

or, {n (n + 1) (2n + 1)/6} / {n (n + 1)/2} = 17

or, (2n + 1)/3 = 17

or, 2n + 1 = 51

or, 2n = 50

∴ n = 25

We have to find, Σ₁ⁿ (2k - 1)

∴ Σ₁²⁵ (2k - 1) [ ∵ n = 25 ]

= 2 (1 + 2 + 3 + ... + 25) - (1 + 1 + ... upto 25 terms)

= 2 * 25 (1 + 25)/2 - 25

= 25 * 26 - 25

= 25 (26 - 1)

= 25 * 25

= 625

∴ option (C) 625 is correct.

Answer 2

Answer:

answer is 625

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