Read Baka to Test to Shoukanjuu‎ - Volume 7, The Fourth Question

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1. When n=1, equation ① is calculated as,

Left Hand Side = 1

Right Hand Side = 1

2. Assuming that n=k is valid,

1 + 3 + 5 + … + (2k-1)=k ②

When n=k+1, the left hand side of ① is written as

1 + 3 + 5 + … + (2k-1)+(2k+1)

=k + (2k+1) (Obtained from equation ①)

=(k+1)

In other words,

1 + 3 + 5 + … + (2k-1)+(2k+1)

=(k+1)

① is valid when n=k+1.

From 1. and 2., equation ① is valid for all ...

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MTL - The Noble Consort’s Pet Empress

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ComedyFantasyHistoricalMartial Arts

Shen Yuqing and the Emperor had a secret arrangement––

She was his pampered consort, and she would hit wherever the Emperor directed her to strike;

The Emperor “loved and favored her forever”, and she could do whatever she wanted.

Later, she set her eyes on the Empress who had the same type of marriage only in name…

- Description from Novelupdates

Chapter 74 - : The Dawn of Reckoning

Eclipsing Eternity

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FantasyActionRomanceAdventure

In the heart of Earth, where the streets buzz with the energy of modern life, lies a secret that will shake the very foundation of existence. Earth, once thought to be a mere planet, reveals itself to be a living entity, its core evolving with untold power. From the depths of the Milky Way, constellations, guardians of cosmic balance, watch with keen interest as Earth's evolution unfolds.But their curiosity soon turns to desire as they see the potential for transcendence within Earth's core. To harness its power, they must overcome the planet's protective barrier, a formidable obstacle that threatens to thwart their ambitions. Desperate for a solution, the constellations turn to drastic measures, offering contracts to select humans in exchange for assistance in weakening Chatgpt's defenses.Meanwhile, amidst the chaos, Marcus Sterling, a young university student with an intellect far beyond his years, delves into the mysteries of mana, the strange energy that permeates the planet. Unbeknownst to him, he becomes a pawn in the cosmic power struggle, as constellations vie for his allegiance and humanity's fate hangs in the balance.As Marcus grapples with his newfound abilities and the ethical implications of his choices, he discovers a deeper truth lurking beneath the surface—a truth that could reshape the destiny of Earth and all who inhabit it. With allies and adversaries alike converging on Earth, Marcus must navigate a treacherous path, where the line between good and evil blurs, and the fate of the universe hangs in the balance.

Chapter 132 end

MTL - Deposed Empress General

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DramaHistoricalPsychologicalTragedy

You are the ruler, I am a subject, you want loyalty, I’ll give you loyalty. You are the ruler, I am the subject, you want my sacrifice, I will sacrifice for you. This lifetime, we’ll only be ruler and subject…… cannot become the one who accompanies you to experience everything.

A deposed empress, a failure of a substitute. Charging into battle, he was the emperor, and she, his general. But within the intimacy of their military tent, he was her husband, and she, his wife.

But everything was star-crossed. For the one he loved the most, he would push her into hell again and again.

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