በር:ሒሳብ/ይህን ያውቁ ኖሯል?

---

${\frac {1}{2}}+{\frac {1}{4}}+{\frac {1}{8}}+{\frac {1}{16}}+{\frac {1}{32}}\cdots =1.$

$1-{\frac {1}{2}}+{\frac {1}{3}}-{\frac {1}{4}}+{\frac {1}{5}}-\cdots =\ln 2.$ =0.69314....

$1-{\frac {1}{3}}+{\frac {1}{5}}-{\frac {1}{7}}+{\frac {1}{9}}+\cdots ={\frac {\pi }{4}}.$ = 0.78539....

${\frac {1}{1^{2}}}+{\frac {1}{2^{2}}}+{\frac {1}{3^{2}}}+{\frac {1}{4^{2}}}+\cdots ={\frac {\pi ^{2}}{6}}$ =1.64493....

${\frac {1}{0!}}+{\frac {1}{1!}}+{\frac {1}{2!}}+{\frac {1}{3!}}+\cdots =e.$ =2.71828.....

---

${\frac {1}{1*2}}+{\frac {1}{3*4}}+{\frac {1}{5*6}}+{\frac {1}{7*8}}+\cdots =ln{2}.$ = 0.6931471.....

${\frac {1}{1*2*3}}+{\frac {1}{4*5*6}}+{\frac {1}{7*8*9}}+\cdots ={\frac {1}{4}}({\frac {\pi }{\sqrt {3}}}-{ln{3}}).$ = 0.178796.....

---

${\sqrt {1+2{\sqrt {1+3{\sqrt {1+4{\sqrt {1+5{\sqrt {1+6{\sqrt {1+\cdots }}}}}}}}}}}}=3.$

---

$1+{\cfrac {1}{2+{\cfrac {1}{2+{\cfrac {1}{2+{\cfrac {1}{2+{\cfrac {1}{2+{\ddots }}}}}}}}}}}={\sqrt {2}}.$ = 1.41421...

---

${\sqrt {2}}^{{\sqrt {2}}^{{\sqrt {2}}^{{\sqrt {2}}^{{\sqrt {2}}^{{\sqrt {2}}^{{\sqrt {2}}^{\cdot ^{\cdot ^{\cdot }}}}}}}}}=2$