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
100 Days to Seduce the DevilChapter 907: The Last Mission: Tracking Her Location
 8.7k
3.9/5(votes)
RomanceJosei

[Warning: R18+] She has to make the Devil fall in love within 100 days to regain her original body!

=======

Phantomflake's soul got separated from her body after committing suicide in front of her enemy, Nathan Sparks, the Supreme Leader of Syphiruz Mafia.

She woke up only to find out that her body (which was in a coma state) was being held captive by Nathan 'the Devil!', who was trying to prolong her life. And what was his motive? To kill her by his own hand and torture her to death!

Nathan has a deep resentment against Phantomflake as she was the one who assassinated the most precious person in his life. He wanted revenge!

And things just got more exciting when a magical creature appeared in front of Phantom's soul, giving her a ridiculous mission in exchange of regaining her body back.

“Make him fall in love with you within 100 days!” The flying creature said, pointing his small paws at Nathan who expressionlessly stood next to her sickbed.

With her eyes going round, Phantomflake made an 'you-got-to-be-kidding-me' face at the flying creature.

No way! That's a mission impossible! This guy loathed her so much. How would she do that??!

******

Excerpt:

“I did everything! Why don't you like me?”

He just shrugged his shoulders and looked at her expressionlessly, making Abigail more annoyed.

Abi: “I cooked for you!”

Nathan: “You almost poisoned me.”

Abi: “I clean your big mansion!”

Nathan: “You broke our century-aged vase family heirloom.”

Abi: “I serenade you!”

Nathan: “You are out of tune.”

Abi: “I took the bullet for you!”

Nathan: “I didn't ask you to do that.”

Abigail squinted her eyes at this cold-hearted devil. She's losing her patience.

Abi: “I almost stripped in front of you but you didn't even react!”

Nathan: “You didn't take all your clothes off.”

Abi: “...”

This time… his lips twitched, smirking at her

Abigail rolled her eyes skyward as she realized that the devil was just teasing her. 'Pervert!'

“Fine. I give up! It's so hard to seduce a robot!” She murmured.

She was about to turn around and leave when suddenly a pair of strong arms caught her by her waist. Then she just felt her body being pushed on the wall.

Nathan's face was now a few centimeters away from hers. She could feel his fresh breath fanning her cheek. “If you want to seduce me then do it properly!”

'Shit! What is he trying to do here?' Abi's heart was thumping like a drum roll inside her chest. Her mind went blank.

Before she knew it, she just found herself being kissed by the devil hungrily and aggressively.

'Damn?! Is this for real? The Devil is kissing me?!'

The Phantom's GambitChapter 103: Devil’s hunt 2
 1k
4.5/5(votes)
FantasyActionComedyMystery

Octavius, misled by friends, embarks on a quest to clear his father's name, ultimately facing a tragic end with his sister.Their journey results in devastating loss, leaving him powerless and yearning for revenge against those who harmed his family. Spirits offer him a chance to reincarnate, but he refuses, saying;“What’s the point of a new life if I keep running from my problems”The entities are taken aback by his unwavering decision, having never encountered a spirit who refuses to escape their troubled past. They warn him about the evil being that now resides in his old body, but that only motivates him. He believed In the saying - to defeat a monster, you have to be twice as monstrous.Embracing his fate as The Phantom's Gambit, they traverse the shadowy path of retribution, their identities blur, secrets unravel, and the line between savior and monster fades.This is a tale of darkness and redemption, where justice is a blade, and revenge is the only way forward.

After Being Transported into a Book, I Adopted the VillainChapter 70: Going Home (2)
 3.8k
4.5/5(votes)
DramaRomanceYaoi

When Shen Yu woke up, he had accidentally gone into a ridiculous dog-blood novel.

In the novel, he is a poor cannon fodder character:

– dead father and mother

– his fiancée had run away

– he is disabled (in a wheelchair)

– he lives a lonely life in a 20,000-square foot mansion.

Later, in order to compete for the female lead, he died under the opposition.

In order to save his life, Shen Yu had to stay as far away as possible from the leading and supporting roles and concentrate on enjoying the luxury life.

As a result, one day, the servant brought a 10-year-old villain with bruised eyes: “Sir, this is the orphan of Tang’s family.”

Shen Yu: “…”

Shen Yu decided to adopt the small villains and change his fate.

Ten Years Later.

The villain pushed Shen Yu to the corner: “Who is that woman?”

Shen Yu: “… Who do you say?”

The villain: “The woman who seduced you at last night’s banquet!”

Shen Yu: “…”

The villain: “Hehe, I’m going to kill her.”

Shen Yu: “My son… That’s the female lead you forgot by the lake…”

MTL - Rebirth Space 80 Little Fierce WifeChapter 441 season finale
 624.1k
3.4/5(votes)
Romance

As soon as Li Siwen opened her eyes, she found that she had traveled to an era when she couldn’t get enough food and clothing, and she was also facing a man who was about to break off the marriage.

Li Siwenle’s divorce, a half-hearted man is not worthy of him.

Although she was depressed looking at this impoverished home, the family members who loved each other warmed her heart.

The key is that she found out that she has supernatural powers, what’s the matter with her power like a cow, and what is the big supermarket in that bracelet? The rice, noodles and meat inside are complete.

The nephews and nieces are hungry, thin and weak, so give them something delicious and delicious to replenish their bodies.

Who else dares to bully their own family, let’s first weigh whether they have the strength to say it!

Shao Qixuan was reborn. He was arrogant and arrogant in his previous life.

In the end, not only was a huge amount of property taken away, but he also contracted an unknown disease at a young age. Everyone avoided it, but the girl who was divorced by himself took care of him for the last time.

In this life, you must keep your eyes open and pamper her.

This article is empty, the heroine is short-tempered, and she will never procrastinate if she has revenge!

- Description from novelbuddy