SOLUTION: 9*10*19+10*11*21+11*12*23+...49*50*99 Find the sum

Algebra ->  Equations -> SOLUTION: 9*10*19+10*11*21+11*12*23+...49*50*99 Find the sum       Log On


   

Question 1029339: 9*10*19+10*11*21+11*12*23+...49*50*99
Find the sum
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!


.
.
.
sum%28n%5E3%2Cn=1%2Ck%29=%281%2F4%29k%5E2%28k%2B1%29%5E2
sum%28n%5E2%2Cn=1%2Ck%29=%281%2F6%29k%28k%2B1%29%282k%2B1%29
sum%28n%5E2%2Cn=1%2Ck%29=k%28k%2B1%29%2F2
.
.
.
sum%28n%5E3%2Cn=1%2C8%29%2Bsum%28n%5E3%2Cn=9%2C49%29=%281%2F4%2949%5E2%2849%2B1%29%5E2
%281%2F4%298%5E2%288%2B1%29%5E2%2Bsum%28n%5E3%2Cn=9%2C49%29=%281%2F4%2949%5E2%2850%29%5E2
1296%2Bsum%28n%5E3%2Cn=9%2C49%29=1500625
sum%28n%5E3%2Cn=9%2C49%29=1499329
.
.
.
sum%28n%5E2%2Cn=1%2C8%29%2Bsum%28n%5E2%2Cn=9%2C49%29=%281%2F6%2949%2850%29%2899%29
%281%2F6%298%289%2917%2Bsum%28n%5E2%2Cn=9%2C49%29=%281%2F6%2949%2850%29%2899%29
204%2Bsum%28n%5E2%2Cn=9%2C49%29=40425
sum%28n%5E2%2Cn=9%2C49%29=40221
.
.
.
sum%28n%2Cn=1%2C8%29%2Bsum%28n%2Cn=9%2C49%29=%281%2F2%2949%2850%29
%281%2F2%298%289%29%2Bsum%28n%2Cn=9%2C49%29=%281%2F6%2949%2850%29%2899%29
36%2Bsum%28n%2Cn=9%2C49%29=1225
sum%28n%2Cn=9%2C49%29=1189
.
.
.
So then putting it all together,

sum%28%28n%28n%2B1%29%282n%2B1%29%29%2Cn=9%2C49%29=+2%2A1499329%2B3%2A40221%2B1189
sum%28%28n%28n%2B1%29%282n%2B1%29%29%2Cn=9%2C49%29=3120510