Loading [MathJax]/jax/output/SVG/jax.js
 
+0  
 
0
702
3
avatar

Compute 1232+1333+1434++11003100

 Feb 28, 2019
 #1
avatar
0

sumfor(n, 1, 100, (1/((n+1)^3 - (n+1)) = 0.2499514657

 Feb 28, 2019
 #2
avatar
0

A slight adjustment in the answer above:

sumfor(n, 1, 99, (1/((n+1)^3 - (n+1)) = 0.249950495 

Guest Feb 28, 2019
 #3
avatar+26396 
+1

Compute

1232+1333+1434++11003100

 

1232+1333+1434++11003100=100n=21n3n=100n=21n(n21)=100n=21n(n1)(n+1)=100n=21(n1)n(n+1)=99n=11n(n+1)(n+2)=99n=11n(n+1)1(n+2)|1n(n+1)=1n1n+1=99n=1(1n1n+1)1(n+2)=99n=11n(n+2)1(n+1)(n+2)|1n(n+2)=12(1n1n+2)=99n=112(1n1n+2)1(n+1)(n+2)|1(n+1)(n+2)=1n+11n+2=99n=112(1n1n+2)(1n+11n+2)=99n=112n12(n+2)1n+1+1n+2=99n=112n1n+1+1n+2(112)=99n=112n1n+1+12(n+2)

 

1232+1333+1434++11003100=99n=112n1n+1+12(n+2)=99n=112n99n=11n+1+99n=112(n+2)=1299n=11n99n=11n+1+1299n=11n+21299n=11n=12+14+1299n=31n=12+14+1297n=11n+299n=11n+1=12+99n=21n+1=12+98n=11n+2=12+97n=11n+2+11001299n=11n+2=1297n=11n+2+12100+12101=12+14+1297n=11n+2(12+97n=11n+2+1100)+1297n=11n+2+12100+12101=12+14+1297n=11n+21297n=11n+21100+1297n=11n+2+12100+12101=141100+12100+12101+1297n=11n+297n=11n+2+1297n=11n+2=141100+12100+12101+97n=11n+297n=11n+2=141100+12100+12101=12(12150+1100+1101)

 

1232+1333+1434++11003100=12(12150+1100+1101)=504920200=0.24995049505

 

laugh

 Mar 1, 2019
edited by heureka  Mar 1, 2019

2 Online Users

avatar