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
Unlimited estates for rural beautyChapter 13 - Cooperation
 90
4.0/5(votes)
HistoricalRomance

Feng Xuxu, a 21st-century professor of agriculture and biology, was in secret the mastermind behind a five-star hotel. Running back and forth between the university and the hotel, it's no wonder she worked herself sick. One moment she closed her eyes, and when she opened them again, she found herself in the body of a poor village girl who had just lost her mother and then her father.Fortunately, time-travel came with a perk, the almighty space ability. After toying with some seeds, she grew thousands of acres of high-yield grains and spent her leisure time cultivating flowers. Before she knew it, she had created a landscape of thousands of acres of flowers. Munching on fruit, she ended up with thousands of acres of orchards. When she craved some greens in the wintertime, she turned around to discover greenhouses covering thousands of acres. Feng Xuxu counted on her fingers: Spring Garden, Summer Garden, Autumn Garden, Winter Garden—not one more, not one less, four in total. She nodded in satisfaction and said, “This is all one needs in life.” Meanwhile, a certain devilishly charming man approached her with a sly smile, “Little Xuxu, how do you plan to deal with me?”Feng Xuxu was in disarray amidst the wind, realizing she had forgotten about one demon yet to be tamed.In this story, both male and female leads are strong, with the male lead being physically and mentally pure and devoted.

MTL - Devouring Is Evolving: My Reincarnation As An Arctic WolfChapter 237 Anthropocene, Theological Union
 412.9k
4.1/5(votes)
Sci-fi

[2022 Science Fiction Starlight Award Word-of-mouth Good Book]

[Third Prize of 2022 Science Fiction Essay]

When a photo of the North Pole taken by a satellite was sent back to various countries, people on earth were shocked by the content of the photo.

They saw thousands of wolves in the North Pole, including hundreds of polar bears and arctic silver foxes, all bowing their heads in unison.

On the top of the snow-capped mountain, a giant arctic wolf whose size exceeds everyone’s imagination is overlooking the arctic ice sheet.

- Description from novelbuddy

Ancestral LineageChapter 345: Ancestral Ascension (3)
 2k
2.5/5(votes)
FantasyActionAdultAdventure

In a realm where power is determined by affinities—elemental forces that shape magic, combat, and survival—Ethan is an anomaly. While most people are born with a single affinity, Ethan stands apart, wielding a vast range of abilities granted by a mysterious Ancestral-line System. This unique system taps into the untapped potential of his vampire and dwarven bloodline, unlocking ancestral powers far beyond the norm.At just 18 years old, Ethan's journey begins when he accidentally awakens this system, discovering that he is the heir to a forgotten lineage that blends the strength, resilience, and mysticism of both vampire and dwarven ancestors, a perfect hybrid of both. Though he must awaken and evolve to harness their power. However, the more power he gains, the more he learns about the dark secrets of his lineage—secrets that others would kill to possess.Unlike everyone else, Ethan's affinities are not innate; they are granted by the system based on his bloodline’s ancient heritage. As he levels up, he acquires abilities that no one in the current era has ever seen: the Psychic powers of telekinesis and telepathy from ancient vampire lords, the earth-shaping skills of dwarf warriors, and a host of hidden abilities that challenge the world’s very understanding of magic.But power comes with a price. Ethan quickly finds himself targeted by powerful factions and hidden enemies who fear what his bloodline could mean for the balance of the world. Ancient forces tied to his ancestry awaken, each with their own agenda—some seeing him as a threat to be eliminated, others as a tool to be used.Accompanied by a diverse group of companions, each with their own affinities and secrets, Ethan embarks on a perilous journey. Together, they traverse beast-filled forests, ancient ruins, worlds and perilous dungeons, all while facing foes who seek to exploit or destroy Ethan’s unique powers. Along the way, bonds are forged, fates are entwined, and the line between friend and foe blurs as Ethan learns that his destiny is far greater than he ever imagined.But with every new ability comes a deeper question: What is the true purpose of the Ancestral-line System? As he battles monstrous creatures, rival affinity users, and ancient curses, Ethan must confront the reality that his bloodline holds the key to either the salvation or the destruction of their world or something else entirely.In a world governed by affinities, Ethan’s unmatched power sets him on a path that could change everything—or lead to his downfall.Will he master the secrets of his ancestry and forge his own fate, or will the weight of his heritage drag him into the depths of a history best left forgotten?

Game Making: Start By Healing the PlayerChapter 60
 297
5.0/5(votes)
AdventureSci-fiComedySlice Of Life

Chen Xu traveled to the parallel world, and was surprised to find that many classic and excellent games in the previous life did not appear in the parallel world.I wanted to make a big picture, but why did I still have an ’emotion collection system’, and the emotions such as happiness, sadness, excitement, fear, anger and other emotions provided by players who have played games made by themselves can make them stronger?But why is it so much easier to get resentment than happiness?Looking at his points harvest, Chen Xu expressed puzzlement.As a result, Chen Xu’s career as a game designer gradually turned crooked.In “Under the Legend”, countless players beat the table and shout: I was played by this game!In “Escape”, countless players shouted, my cabinet moved, and I stopped playing.In “Dark Souls”, when countless players entered the game with a smile, “Go away, please go away, leave the fire girl behind and go out with your fire, we don’t want to spread this fire!”Soap, Xiaoqiang, and Ghost sacrificed in “Call of Duty”; Zack was killed and Alice was killed in “Final Fantasy 7”; Arthur and John were betrayed in “Red Dead Redemption”;Countless players went berserk: Nima Chen Xu old thief, can’t we be kinder to the protagonist?Q: How do I feel about players’ anger towards themselves?Facing the reporter’s question, Chen Xu smiled slightly: What kind of verbal criticism is this, this is the encouragement of players around the world to me, this is love! Thank you all, I will keep up the good work!