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
Gates of PenanceChapter 33: Man in the mirror
 359
5.0/5(votes)
FantasyActionAdventureMystery

Penance is a prison of eternal damnation for those who go against the will of the gods.Growing up in the slums of District Nine, Nacht was like every other individual his age, struggling to survive with what little he had and blaming the capital for it. But unlike everyone else, he had been lucky. He still had a mother who cared for him deeply and did everything she could to help him succeed. However, that all changed when his mother was offered up as a sacrifice to the capital to help bolster the number of Enlightened in their arsenal.The Enlightened were elite warriors who wielded supernatural powers and served their respected clan at the cost of sacrificing an individual for the opportunity to enter Penance and be bestowed or awakening a rune, the source of their profound power.Having been exposed to the worst of humanity due to the horrific execution of his mother, Nacht developed a relentless ambition to change the world—even if it was in his own unconventional way.After performing a disgraceful ritual, Nacht is sent into Penance, where he becomes one of the Enlightened and is bestowed a mysterious power along with an insidious punishment.

MTL - Six-Year-Old Child, Baojiao, is Busy with Kingdom-BuildingChapter 494 Epilogue End
 995.4k
4.8/5(votes)
Romance

[Group Pet + Farming]

The little ginseng essence was finally shaped into a human figure, but was smashed to pieces by Wang Baojiao who slipped and fell into the pool. When she woke up, she was lying on the earthen kang of the Wang family, and many people around the kang looked at her distressedly.

The shrewd woman put her hands on her hips: “My Jiaojiao, who the hell pushed you into the river!”

The strong man’s father cried and cried: “Jiaojiao, if you don’t wake up, Dad will go with you.”

Eldest brother who is frail and sick: “Little sister, I won’t go to school anymore, I will always be by your side to protect you in the future.”

The black girl with sky braids: “Little sister, be good~ Second sister will buy you a hair tie.”

The silly third brother sucking snot: “Sister~ I will give you all the bird eggs my little brother digs out.”

Facing poor and decrepit family members who are plagued by bad luck, the small ginseng essence waved its fat hand, and the century-old ginseng spirit whiskers, one for you, the other will remove the bad luck, bring good fortune, and cure all diseases!

A family of six, the days are getting more and more prosperous.

Many years later, Jiaojiaobao reached the age of marriage. Everyone in the Wang family was very worried, thinking that no one could match their own Jiaojiao.

Unexpectedly, Jiaojiao brought back a beautiful boy by herself, and said that he was her future husband-in-law.

The master of the national teacher who retired from the world was not close to women, but he didn’t want to be disturbed by a little ginseng spirit.

- Description from novelbuddy

Solar MageChapter 84: Final Announcement and pause
 623
2.8/5(votes)
FantasyAdventure

Arthur Ventrike, a genius second-year at the prestigious Wolkan Royal Academy, hailed to be the most talented in his generation, reaches the Swordsman stage of Knight at just 15 under Grandmaster Thorne Bladesong. But envy strikes when a fifth-year student tries to poison him. Though the plot fails, Arthur is left crippled, his dreams shattered. Just when all hope seems lost, he inherits a Great Sage’s legacy and sets out to become the greatest wizard along with the blessing of an indecent goddess and save the world from an ancient evil.

Transmigration: Flirted with My Childhood SweetheartChapter 936 - 931: Su Ziyue (Grand Finale)
 5.8k
4.5/5(votes)
RomanceSlice Of Life

Lin Nianhe, the leading lady of the apocalypse, came equipped with a top-tier space, furiously hoarded tens of billions of resources, and then — she traveled through time!The first day, a fierce squabble unfolded;The second day, the production team's competition for overachievement was fiery hot;The third day…Lin Nianhe: “Comrades, be inspiring!”The crowd, struggling: “Hardworking guy, stop brewing motivational speeches.”Lin Nianhe: “All the aunties are so adorable!”The production team's aunties, hearts shattered: “Xiao Lin has hogged all the brains in her family.”Lin Nianhe relished in dramas, smashing feet with excitement, as she performed her new script brilliantly.The swap of resources made her little treasure chest increasingly rich;Tailored teaching, students acing their exams with full marks!Lin Nianhe, with education in her left hand and economy in her right, ignited the darkness with sparks of light.The first time Su Yuncheng was asked when he would tie the knot with Lin Nianhe, he said, “Let me first win over her parents.”The second time Su Yuncheng was asked when they could taste the wedding candy, he answered, “Wait until I've conquered her dozen or so siblings.”The third time Su Yuncheng was questioned about his relationship progress with Lin Nianhe, he replied, “Our relationship is stable, but the entire village of three hundred, young and old, are all trying to snatch her from me.”He then turned around, pitifully searching for his delicate childhood sweetheart: “Hehe, when will you make it formal with me?”Lin Nianhe responded offhandedly: “Wait till I finish building this batch of schools.”The next day, Lin Nianhe discovered that the sites she'd chosen for the schools had already started construction overnight![Cool community leader · Unknowingly charming · Little drama queen × Cunning · Self-challenger · Big friendly dog]