5+11+19+29+41+....

Asked by pavanindr | 9th Feb, 2020, 04:56: PM

Expert Answer:

5+11+19+29+41+....
Let space
straight S equals space 5 plus 11 plus 19 plus 29 plus 41 plus.... open parentheses 1 close parentheses
straight S equals 0 plus space 5 plus 11 plus 19 plus 29 plus 41 plus.. plus straight a subscript straight n.. open parentheses 2 close parentheses
sub space open parentheses 1 close parentheses minus open parentheses 2 close parentheses
0 space equals space 5 space plus open parentheses 11 minus 5 close parentheses plus open parentheses 19 minus 11 close parentheses plus... negative straight a subscript straight n
straight a subscript straight n equals 5 plus open parentheses 6 plus 8 plus 10 plus... left parenthesis straight n minus 1 right parenthesis space terms close parentheses
straight a subscript straight n equals 5 plus open parentheses straight n minus 1 close parentheses left parenthesis straight n plus 4 right parenthesis......................6 plus 8 plus 10 plus... left parenthesis straight n minus 1 right parenthesis space is space sum space of space AP
straight a subscript straight n equals straight n squared plus 3 straight n plus 1
apply space summation space to space each space terms space straight n equals 1 space to space straight n
straight S equals sum from straight n equals 1 to straight n of straight n squared plus 3 sum from straight n equals 1 to straight n of straight n plus sum from straight n equals 1 to straight n of 1
apply space the space formulas

Answered by Arun | 14th Feb, 2020, 12:45: PM