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Question Number 145809 by puissant last updated on 08/Jul/21
prove 1+2+3+.....=−(1/(12))
prove1+2+3+…..=−112
Answered by Olaf_Thorendsen last updated on 09/Jul/21
A = 1−1+1−1+1−... A = 1−(1−1+1−1+1−...) A = 1−A A = 1/2 B = 1−2+3−4+5−6+7+... B = 1−(2−3+4−5+6−7+...) B = 1−(1−2+3−4+5−6+...) −(1−1+1−1+1−1+...) B = 1−B−A B = 1/4 S = 1+2+3+4+5+6+... S−B = (1+2+3+4+5+6+...) −( 1−2+3−4+5−6+7+...) S−B = 2∗(2+4+6+8+...) S−B = 4∗(1+2+3+4+...) = 4S S = −B/3 S = −1/12 !
A=1−1+1−1+1−…A=1−(1−1+1−1+1−…)A=1−AA=1/2B=1−2+3−4+5−6+7+…B=1−(2−3+4−5+6−7+…)B=1−(1−2+3−4+5−6+…)−(1−1+1−1+1−1+…)B=1−B−AB=1/4S=1+2+3+4+5+6+…S−B=(1+2+3+4+5+6+…)−(1−2+3−4+5−6+7+…)S−B=2∗(2+4+6+8+…)S−B=4∗(1+2+3+4+…)=4SS=−B/3S=−1/12!
Commented by puissant last updated on 09/Jul/21
thank you sir
thankyousir

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