The sum 3 × 1 3 1 2 + 5 × ( 1 3 + 2 3 ) 1 2 + 2 2 + 7 × ( 1 3 + 2 3 + 3 3 ) 1 2 + 2 2 + 3 2 + . . . . . upto 10 t h term is

Question

The sum 3 &#215; 1 3 1 2 + 5 &#215; ( 1 3 + 2 3 ) 1 2 + 2 2 + 7 &#215; ( 1 3 + 2 3 + 3 3 ) 1 2 + 2 2 + 3 2 + . . . . . upto 10 t h term is

Aicharya · Accepted Answer

S = &#160; 3 1 3 12 + 5 1 3 + 2 3 1 2 + 2 2 + 7 1 3 + 2 3 + 3 3 1 2 + 2 2 + 3 2 + &#8230; 10 &#160; t e r m s Here the general terms is T r = 2 r + 1 1 3 + 2 3 + &#8230; . + r 3 1 2 + 2 2 + &#8230; . + r 2 + 2 r + 1 r r + 1 2 2 r r + 1 2 r + 1 6 = 3 2 &#160; r ( r + 1 ) &#8658; S = &#8721; r = 1 10 3 2 r r + 1 = 3 2 &#8721; r = 1 10 r 2 + &#8721; r = 1 10 r = 3 2 10.11.21 6 + 10.11 2 = 3 2 385 + 55 = 660

The sum 3 × 1 3 1 2 + 5 × ( 1 3 + 2 3 ) 1 2 + 2 2 + 7 × ( 1 3 + 2 3 + 3 3 ) 1 2 + 2 2 + 3 2 +…

Solution

The sum 3 &#215; 1 3 1 2 + 5 &#215; ( 1 3 + 2 3 ) 1 2 + 2 2 + 7 &#215; ( 1 3 + 2 3 + 3 3 ) 1 2 + 2 2 + 3 2 +…

Solution

The sum 3 × 1 3 1 2 + 5 × ( 1 3 + 2 3 ) 1 2 + 2 2 + 7 × ( 1 3 + 2 3 + 3 3 ) 1 2 + 2 2 + 3 2 +…