1−1+1−1+1−1+1−1+.....=(1/2) {But it diverges 1+1+1+1+1+1+1+......=−(1/2) {But it diverges 1+2+4+8+16+.....=−1 {But it diverges 1+2+3+4+5+6+7=−(1/(12)) {But it diverges 1−2+4−8+.....=(1/3) {But it diverges 1−2+3−4+5−6+.....=(1/4) {Is it a divergent?????


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Question Number 102745 by Dwaipayan Shikari last updated on 10/Jul/20

$1 - 1 + 1 - 1 + 1 - 1 + 1 - 1 + . . . . . = \frac{1}{2} {B u t i t d i v e r g e s$ $1 + 1 + 1 + 1 + 1 + 1 + 1 + . . . . . . = - \frac{1}{2} {B u t i t d i v e r g e s$ $1 + 2 + 4 + 8 + 16 + . . . . . = - 1 {B u t i t d i v e r g e s$ $1 + 2 + 3 + 4 + 5 + 6 + 7 = - \frac{1}{12} {B u t i t d i v e r g e s$ $1 - 2 + 4 - 8 + . . . . . = \frac{1}{3} {B u t i t d i v e r g e s$ $1 - 2 + 3 - 4 + 5 - 6 + . . . . . = \frac{1}{4} {I s i t a d i v e r g e n t ? ? ? ? ?$
Commented by Dwaipayan Shikari last updated on 10/Jul/20

$F u n n y g r e a t s e q u e n c e s$
Commented by prakash jain last updated on 10/Jul/20
See the link below to get an idea behind theory for calculating these sum of divergent series. https://en.m.wikipedia.org/wiki/Analytic_continuation also this link given some additional info about other summation methods https://en.m.wikipedia.org/wiki/Divergent_series
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