5 If 1 1 4 + 1 2 4 + 1 3 4 + + ∞ = π 4 90 , then the value of 1 1 4 + 1 3 4 + 1 5 4 + + ∞ is

HI, 114+124+134+ ∞=π490114+134+154+ ∞+124+144+164+ ∞=π490114+134+154+ ∞+124114+124+134+ ∞=π490114+134+154+ ∞+124π490=π490114+134+154+ ∞=π490-124π490=π4901-124=1516×π490=π496

5. If $\frac{1}{1^{4}} + \frac{1}{2^{4}} + \frac{1}{3^{4}} + . . . + \infty = \frac{π^{4}}{90}$ , then the value of $\frac{1}{1^{4}} + \frac{1}{3^{4}} + \frac{1}{5^{4}} + . . . + \infty$ is

HI, \frac{1}{1^{4}} + \frac{1}{2^{4}} + \frac{1}{3^{4}} + . . . . . . . \infty = \frac{π^{4}}{90} (\frac{1}{1^{4}} + \frac{1}{3^{4}} + \frac{1}{5^{4}} + . . . . . . . \infty) + (\frac{1}{2^{4}} + \frac{1}{4^{4}} + \frac{1}{6^{4}} + . . . . . . . \infty) = \frac{π^{4}}{90} (\frac{1}{1^{4}} + \frac{1}{3^{4}} + \frac{1}{5^{4}} + . . . . . . . \infty) + \frac{1}{2^{4}} (\frac{1}{1^{4}} + \frac{1}{2^{4}} + \frac{1}{3^{4}} + . . . . . . . \infty) = \frac{π^{4}}{90} (\frac{1}{1^{4}} + \frac{1}{3^{4}} + \frac{1}{5^{4}} + . . . . . . . \infty) + \frac{1}{2^{4}} (\frac{π^{4}}{90}) = \frac{π^{4}}{90} (\frac{1}{1^{4}} + \frac{1}{3^{4}} + \frac{1}{5^{4}} + . . . . . . . \infty) = \frac{π^{4}}{90} - \frac{1}{2^{4}} (\frac{π^{4}}{90}) = \frac{π^{4}}{90} [1 - \frac{1}{2^{4}}] = \frac{15}{16} \times \frac{π^{4}}{90} = \frac{π^{4}}{96}

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5. If 1 1 4 + 1 2 4 + 1 3 4 + . . . + ∞ = π 4 90 , then the value of 1 1 4 + 1 3 4 + 1 5 4 + . . . + ∞ is

5. If $\frac{1}{1^{4}} + \frac{1}{2^{4}} + \frac{1}{3^{4}} + . . . + \infty = \frac{π^{4}}{90}$ , then the value of $\frac{1}{1^{4}} + \frac{1}{3^{4}} + \frac{1}{5^{4}} + . . . + \infty$ is