# IPMAT Question Paper 2020 | IPM Indore Quants

###### IPMAT Sample Paper | IPMAT Question Paper | Question 15

IPMAT 2020 Question Paper IPM Indore Quantitative Ability. Solve questions from IPMAT 2020 Question Paper from IPM Indore and check the solutions to get adequate practice. The best way to ace IPMAT is by solving IPMAT Question Paper. To solve other IPMAT Sample papers, go here: IPM Sample Paper

Question 15 : If $$frac{1}{1^{2}}$ + $\frac{1}{2^{2}}$ + $\frac{1}{3^{2}}$ + .... upto ∞ = $\frac{π^{2}}{6}$, then the value of $\frac{1}{1^{2}}$ + $\frac{1}{3^{2}}$ + $\frac{1}{5^{2}}$ + .... upto ∞ is 1. $\frac{π^{2}}{8}$ 2. $\frac{π^{2}}{16}$ 3. $\frac{π^{2}}{12}$ 4. $\frac{π^{2}}{36}$ ## Best CAT Online Coaching Try upto 40 hours for free Learn from the best! #### 2IIM : Best Online CAT Coaching. ### Video Explanation ## Best CAT Coaching in Chennai #### CAT Coaching in Chennai - CAT 2022Limited Seats Available - Register Now! ### Explanatory Answer $\frac{1}{1^{2}}$ + $\frac{1}{2^{2}}$ + $\frac{1}{3^{2}}$ + .... upto ∞ = $\frac{π^{2}}{6}$ $\frac{1}{1^{2}}$ + $\frac{1}{3^{2}}$ + $\frac{1}{5^{2}}$ + .... + Δ = $\frac{π^{2}}{6}$ This Δ is nothing but $\frac{1}{2^{2}}$ + $\frac{1}{4^{2}}$ + $\frac{1}{6^{2}}$ + .... All these terms are even numbers and hence we can take $\frac{1}{2^{2}}$ common out, Δ = $\frac{1}{2^{2}}$ + $\frac{1}{4^{2}}$ + $\frac{1}{6^{2}}$ + .... Δ = $\frac{1}{2^{2}}$ { $\frac{1}{1^{2}}$ + $\frac{1}{2^{2}}$ + $\frac{1}{3^{2}}$ + .... } Δ = $\frac{1}{2^{2}}$ { $\frac{π^{2}}{6}$ } Δ = $\frac{1}{4}$ { $\frac{π^{2}}{6}$ } Since, $\frac{1}{1^{2}}$ + $\frac{1}{3^{2}}$ + $\frac{1}{5^{2}}$ + .... + Δ = $\frac{π^{2}}{6}$ $\frac{1}{1^{2}}$ + $\frac{1}{3^{2}}$ + $\frac{1}{5^{2}}$ + .... = $\frac{π^{2}}{6}$ - Δ $\frac{1}{1^{2}}$ + $\frac{1}{3^{2}}$ + $\frac{1}{5^{2}}$ + .... = $\frac{π^{2}}{6}$ - $\frac{1}{4}$ { $\frac{π^{2}}{6}$ } $\frac{1}{1^{2}}$ + $\frac{1}{3^{2}}$ + $\frac{1}{5^{2}}$ + .... = $\frac{3}{4}$ { $\frac{π^{2}}{6}$ } = $\frac{π^{2}}{8}$ ##### The answer is $\frac{π^{2}}{8}$ Choice A is the correct answer. ###### Best Indore IPM & Rohtak IPM CoachingSignup and sample 9 full classes for free. Register now! ###### Already have an Account? ##### Where is 2IIM located? 2IIM Online CAT Coaching A Fermat Education Initiative, 58/16, Indira Gandhi Street, Kaveri Rangan Nagar, Saligramam, Chennai 600 093 ##### How to reach 2IIM? Mobile:$91) 99626 48484 / 94459 38484
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