PREVIEW

... er

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 ...

YOU MAY ALSO LIKE
Lord ShadowChapter 1877 Crazy Idea
 11.9k
3.3/5(votes)
FantasyActionAdventureRomance

In the aftermath of apocalyptic event, a man rises above the others to lead an era.

With threat beyond the stars, as Supreme Beings of otherworldly star system watches over as Destiny and Fate work their way, an era of Gods descended upon Earth

And in his rise, lies a terrifying secret. Read how he rises above it all, through all the complicated love life, his determination to push through his own fate and destiny and the Will that pushes him forward.

With all of this, could the Fate that was written be overturned? And will he truly rise to the top and survive?

A great battle for the fate of the Universe began.

This is the story of Lord Shadow.

The Deceitful OneChapter 108 Perfect Place For Murder
 505
5.0/5(votes)
FantasyAdventureReincarnation

With the advent of steam power, mankind has advanced and ushered in the industrial revolution. This is the age of steam locomotives, guns, and cannons, as well as curses, magic, artifacts, and the supernatural.

Hidden in the shadows are a group of extraordinary people who wield enormous power and strange abilities that normal people cannot even begin to comprehend. They are known as Transcendents!

Bryan lost his parents at a very young age and was forced to live on the streets. That is until his whole life turned around when he was shown the Path to becoming a Transcendent.

The Theft Path specializes in deceit and illusions. It can steal everything under the heavens. Even the powers, thoughts, and dreams of others.

Follow Bryan on his journey through this dangerous and treacherous world as he steals from gods and robs the mortals.

This is the story of The Deceitful One.

Rise of the Primordial Dragon beast tamerChapter 65 - : Sparks of Determination.
 394
4.5/5(votes)
FantasyActionAdventure

A thousand years ago, the world shattered.Mana surged into existence, rewriting reality itself. Dungeons tore through the land, birthing monstrous horrors, while beasts mutated under the influence of Primordial Ki, evolving into unstoppable apex predators. Humanity was on the brink of annihilation—until the Awakened emerged, wielding supernatural power to defy extinction.Yet, in this brutal new world, strength reigns supreme, and weakness is a death sentence.Amidst it all, Azvoid Larkson—a nameless figure among the countless struggling to survive—awakens a power beyond reason. A power tied to ancient, forgotten dragons—beasts feared even by the strongest Awakened.With each battle, he ascends. With every dragon he tames, his legend grows.In a world where only the strong thrive, how far can one man rise?

Supreme Archer: Taking The Game's Weakest Class To The TopChapter 303: The Oath Kingdom (END)
 955
5.0/5(votes)
GameAdventureActionComedy

“You're worth a single arrow.”The first immersive virtual MMORPG, The Legend Enigma Online, has conquered the game market! There's not even one person who hasn't heard or seen this game's beautiful and vast magical world overflowing with monsters.Everyone wanted to play this game and be a part of history!Conjuring magic, wielding enormous swords, and even flying across the skies are possible in this game! Guns, arrows? Those are boring compared to this!Jake, however, was compelled to think differently.When the archery became abandoned and forgotten, he took this class and swore to prove others wrong, all because he likes to go against the mainstream!With the bow in his hand, Jake finds passion, talent, and excitement in archery, but will that be enough against the challenges the world keeps for him?It's not only the players that find archery weaker than magic. After the dawn of mana, which happened over two hundred years ago, even NPCs prefer magic over bows.While the other classes have been developed so much by NPCs that players have many luxuries to pick from, the archery is now a mere shadow of its past.That's only the tip of the iceberg of the future Supreme Archer's difficulties!“No matter whatever it is and how long it takes, I'll take everything on and get my archery to the top! The archery where I'm the master and artisan of my bows and arrows, the tailor of my equipment, and pioneer of my own skills!”Hard work, talent, bitter defeats, and uproarious victories–none of it is foreign to Jake!