Sum of term:

1^3+3^3+5^3+7^3....

Asked by vasaya.sohil99 | 24th Sep, 2019, 11:16: AM

Expert Answer:

1 cubed plus 3 cubed plus 5 cubed plus... plus left parenthesis 2 n minus 1 right parenthesis cubed space equals open parentheses 1 cubed plus 2 cubed plus 3 cubed plus 4 cubed plus... plus left parenthesis 2 n right parenthesis cubed close parentheses minus open parentheses 2 cubed plus 4 cubed plus.... plus left parenthesis 2 n right parenthesis cubed close parentheses
equals open parentheses 1 cubed plus 2 cubed plus 3 cubed plus 4 cubed plus... plus left parenthesis 2 n right parenthesis cubed close parentheses minus 2 cubed open parentheses 1 cubed plus 2 cubed plus.... plus n cubed close parentheses
equals sum from k equals 1 to 2 n of space k cubed minus 8 sum from k equals 1 to n of space k cubed
equals fraction numerator left parenthesis 2 n right parenthesis squared left parenthesis 2 n plus 1 right parenthesis squared over denominator 4 end fraction minus 8 fraction numerator n squared left parenthesis n plus 1 right parenthesis squared over denominator 4 end fraction
equals n squared left parenthesis 2 n squared minus 1 right parenthesis
A s space n rightwards arrow infinity comma space t h e space s u m space t e n d s space t o space infinity

Answered by Renu Varma | 3rd Oct, 2019, 11:24: AM