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
My Game's NPC Girlfriend Has Come To The Real WorldChapter 80 - 79: Bigger is Better
 954
4.5/5(votes)
FantasyRomanceMysteryHarem

Xu Mo loved playing games on Steam and bought a ton of them. But he soon realized something strange—whatever happened in the game started affecting his real life!When he played as an AI girl, a gorgeous girlfriend appeared in the real world. After robbing a bank in GTA, millions of dollars showed up in his real bank account.One time, while exploring a fantasy game, a Taoist monk with incredible powers showed up in reality, cutting an aircraft carrier in half with a sword and talking to him about Taoism.Things quickly spiraled out of control, throwing the whole world into chaos!

Type-Moon Simulation: Starting with Conquering a Greek Goddess!Chapter 620: Unpreventable Accidents
 4.4k
4.5/5(votes)
FantasyRomanceAdultAdventure

The Pseudo-Holy Grail War of Snowfield is About to Begin!Moran, who has transmigrated into the Type-Moon universe, is determined to clear the game in one life!Waiting online, urgent!Ding! You have successfully activated the Life Simulator!• 【You drove out the foreign Olympian Machine Gods, took the hand of the Earth Mother Goddess, and founded a new nation and mythology.】• 【You are the Lord of the Millennium Castle, bestowed with the name Brunestud, and the beloved ruler of the land in the eyes of the Crimson Moon.】• 【You are the Final King of the Age of Gods, single-handedly preventing its decline and ensuring that Divine Age Britain endures to this day.】Behind this dazzling simulated life, Moran now faces—Arcueid: “Weren’t you supposed to pick me up at the Millennium Castle? Why are you here in the Holy Grail War?!”Artoria: “Enough! Come back to Britain with me!”Ereshkigal: “Moran! Who are all these women?!”As his ever-growing circle of admirers closes in, Moran realizes—This might just be the hardest “Kidney Grail War” in history.

MTL - Cultivating In Secret Beside A DemonessChapter 707 locked up
 621.1k
3.3/5(votes)
FantasyXianxia

Jiang Hao passed through ordinary people and was forced to be sold into the Demon Sect and became a disciple of the Demon Sect.

I wanted to cultivate with peace of mind to become stronger a little bit so that I could survive in the world of self-cultivation, but was “humiliated” by a female devil in every possible way.

There is a huge disparity in strength, and he can only endure the humiliation and survive, hoping not to meet each other again.

Without a backer, he was favored by the Demon Sect’s headmaster and was able to practice with peace of mind. When he became the chief disciple and met the headmaster, he was stunned.

Looking at the beautiful face of the other party, he couldn’t smile a little. Isn’t this the female devil?

- Description from novelbuddy

Paragon of DeathChapter 325 - : Fear Death!
 2.7k
3.4/5(votes)
ActionAdventureFantasyHarem

Life from birth has been nothing but hell. I lost my parents to some stupid aristocrats whom they offended. Executed for no good reason.

My relatives abandoned me and pushed me aside. They feared for their lives and left me and my sister to starve and wander the streets alone!

No, this is worse than hell!

I watched my sister die of starvation. Her lips were dry and her feet bloody. Her nails were broken and her fingers riddled with cuts. She struggled in my hands and after a few seconds of struggle she passed away. She seemed joyful in death so I prayed mine will come just as swift and merciful as hers.

So I stayed in the alleyway, alone with her rotten corpse awaiting my fate for God knows how long. I could see it already. The darkness encroaching from all sides

Everyone said death is scary but I say it’s the end! Who needs life after death? What is the need for reincarnation?

Who would want to return to this crazy world?

“It’s not yet time for you to go… You have one more task to accomplish as my host” A voice called out to me.

I could barely see or speak but how can I miss such a beautiful face? It was an extremely handsome man who gazed at me with tender eyes.

.....

“Haven’t I suffered enough? Can’t I just rest?” I cried out. Why would I want to stay back in such a cruel world?

“Don’t you want to avenge the death of your parents? Don’t you want to become something greater? I can make that happen!” The beautiful man said with an alluring voice.

“You… Who are you?” I asked with an anxious heart.

My parents always said God is the only one who cares about me! Maybe in my final hours, he has come to save me.

“Call me Death…”