MathDB

22

Part of 2019 India PRMO

Problems(2)

Telescoping Sum

Source:

8/11/2019
What is the greatest integer not exceeding the sum ∑n=115991n\sum^{1599}_{n=1} \dfrac{1}{\sqrt{n}}?
telescoping sums
Trig Geometry

Source: PRMO Leg 2 P22

8/25/2019
In parallelogram ABCDABCD, AC=10AC=10 and BD=28BD=28. The points KK and LL in the plane of ABCDABCD move in such a way that AK=BDAK=BD and BL=ACBL=AC. Let MM and NN be the midpoints of CKCK and DLDL, respectively. What is the maximum walue of cot⁡2(∠BMD2)+tan⁡2(∠ANC2)\cot^2 (\tfrac{\angle BMD}{2})+\tan^2(\tfrac{\angle ANC}{2}) ?
trigonometrygeometryPRMO