Can You Find My Forever?

Algebra Level 4

Which of the following is the forever sum of π 4 \frac{ \pi}{4} .

Details

Forever sum means infinite series equivalent .

1 − ( 1 / 3 ) + ( 1 / 5 ) − ( 1 / 7 ) . . . . 1-(1/3)+(1/5)-(1/7).... 1 + ( 1 / 2 ) + ( 1 / 4 ) + ( 1 / 8 ) . . . . . . 1+ (1/2) + (1/4) + (1/8)...... 1 + ( 1 / 4 ) + ( 1 / 9 ) + . . . . . 1+(1/4) + (1/9) + ..... none of the choices 1 + ( 1 / 2 ) − ( 1 / 3 ) + ( 1 / 4 ) + . . . . 1+(1/2) - (1/3) + (1/4) +....

Paul Ryan Longhas by Paul Ryan Longhas , 24, Philippines

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2 solutions

Prakhar Gupta
Apr 7, 2015

Writing the Taylor series of tan ⁡ − 1 x \tan^{-1}x . tan ⁡ − 1 x = x − x 3 3 + x 5 5 … \tan^{-1}x = x - \dfrac{x^{3}}{3}+\dfrac{x^{5}}{5} \ldots Put x = 1 x = 1 . π 4 = 1 − 1 3 + 1 5 … \dfrac{\pi}{4} = 1-\dfrac{1}{3} + \dfrac{1}{5} \ldots

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Paul Ryan Longhas
Feb 21, 2015

The solution can be see in this problem

See...

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