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IPMAT Indore 2025 · Question 23 of 90 · Quantitative Ability (MCQ)

IPMAT Indore 2025 — Question 23

Given that $1 + \frac{1}{2 ^{2}} + \frac{1}{3 ^{2}} + \frac{1}{4 ^{2}} + \dots = \frac{π ^{2}}{6}$ , the value of $1 + \frac{1}{3 ^{2}} + \frac{1}{5 ^{2}} + \frac{1}{7 ^{2}} + \dots$ is

A $\frac{π ^{2}}{6} - 1$
B $2 \frac{π}{6}$
C $\frac{π ^{2}}{8}$
D $\frac{π ^{2}}{12}$

Reveal answer

Correct answer

C.

\frac{π ^{2}}{8}

Reveal solution

Split the original sum into odd-only and even-only parts. The even-only sum equals $\frac{1}{4} \cdot \frac{π ^{2}}{6}$ . The odd-only sum = $\frac{π ^{2}}{6} - \frac{π ^{2}}{24} = \frac{π ^{2}}{8}$ .

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