Question

20. If the sum of first n natural numbers is 1/78 times the sum of their cubes, then the value of n is :
(a) 11
(b) 12
(c) 13
(d) 14​

Answer 1

$\huge{\boxed{\overline{\underline{\mathfrak{\fcolorbox{cyan}{blue}{Answer}}}}}}$

=> n = 12

Given, the sum of first n natural numbers = 1/78 (the sum of their cubes)

=> n(n+1)/2 = 1/78 × n²(n+1)²/4

=> 156 = n²(n+1)²

=> n²+n - 156 = 0

=> (n + 13)(n - 12) = 0

=> n = 12 (n = -13 is negative)

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Answer 2

$\implies$ options no (b)