Explore

Leibniz Series

Gottfried Wilhelm Leibniz · 1676 · Germany
π4=∑k=0∞(−1)k2k+1\frac{\pi}{4}=\sum_{k=0}^{\infty}\frac{(-1)^k}{2k+1}

The simplest series for pi: an alternating sum of odd reciprocals. It converges very slowly — thousands of terms are needed for even a few digits of accuracy.

0 Term
4.000000000000000 Estimate
0 Correct digits
8.584e-1 Error
01TermCorrect digits
3 .
1415926535897932384626433832795028841971693993751058209749445923078164062862089986280348253421170679
0 digits correct