Question

Find the period of the function: tan (x + 4x +9x + ... + n²x) (n is any positive integer

Answer 1

we have to find period of function , tan(x + 4x + 9x + ...... n²x)

first of all, solve (x + 4x + 9x + ..... + n²x)

x + 4x + 9x + ....... + n²x = x[ 1 + 4 + 9 + .... + n²]

= x[1² + 2² + 3² + ....... + n²]

= x [ n(n + 1)(2n + 1)/6 ]

= n(n + 1)(2n + 1)x/6

so, we have to find period of function , tan[n(n + 1)(2n + 1)x/6 ]

we know, period of tanax is $\frac{\pi}{|a|}$

so, period of tan[n(n + 1)(2n + 1)x/6 ] is π/[n(n + 1)(2n + 1)/6] or, 6π/{n(n + 1)(2n + 1)}

Answer 2

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