The sum of the following series 1 + 6 + 9 1 2 + 2 2 + 3 2 7 + 12 1 2 + 2 2 + 3 2 + 4 2 9 + 15 ( 1 2 + 2 2 + … + 5 2 ) 11 + . . . . up to 15 terms, is:

Question

The sum of the following series 1 + 6 + 9 1 2 + 2 2 + 3 2 7 + 12 1 2 + 2 2 + 3 2 + 4 2 9 + 15 ( 1 2 + 2 2 + &#8230; + 5 2 ) 11 + . . . . up to 15 terms, is:

Aicharya · Accepted Answer

t n = 3 n 1 2 + 2 2 + 3 2 + &#8230; + n 2 2 n + 1 = 3 n &#215; n n + 1 2 n + 1 6 &#160; 2 n + 1 = 1 2 &#160; n 3 + n 2 &#8756; S 15 = &#8721; n = 1 15 t n = &#8721; n = 1 15 1 2 n 3 + n 2 = 1 2 &#8721; n = 1 15 n 3 + &#8721; n = 1 15 n 2 = 1 2 &#215; 15 &#215; 16 2 2 + 15 &#215; 16 &#215; 31 6 &#160; &#8721; n 3 = n n + 1 2 2 , &#160; &#8721; n 2 = n n + 1 n + 2 6 = 7200 + 620 = 7820

The sum of the following series 1 + 6 + 9 1 2 + 2 2 + 3 2 7 + 12 1 2 + 2 2 + 3 2 + 4 2 9 + 15 ( 1 2 + 2 2 +…

Solution