question is attached. Please send step by step complete solution.

Asked by sudhanshubhushanroy | 10th Dec, 2017, 03:55: AM

Expert Answer:

begin mathsize 16px style straight S subscript straight n equals straight a subscript straight n left parenthesis straight n minus 1 right parenthesis space
rightwards double arrow straight S subscript straight n minus 1 end subscript equals straight a left parenthesis straight n minus 1 right parenthesis space open parentheses straight n minus 2 close parentheses
straight t subscript straight n equals straight S subscript straight n minus straight S subscript straight n minus 1 end subscript
straight t subscript straight n equals straight a subscript straight n left parenthesis straight n minus 1 right parenthesis minus straight a left parenthesis straight n minus 1 right parenthesis space open parentheses straight n minus 2 close parentheses
straight t subscript straight n equals 4 straight a squared open parentheses straight n minus 1 close parentheses squared
sum for straight n of straight t subscript straight n squared equals 4 straight a squared open parentheses fraction numerator left parenthesis straight n minus 1 right parenthesis left parenthesis straight n minus 1 plus 1 right parenthesis open square brackets 2 left parenthesis straight n minus 1 right parenthesis plus 1 close square brackets over denominator 6 end fraction close parentheses
equals 4 straight a squared open parentheses fraction numerator straight n left parenthesis straight n minus 1 right parenthesis left parenthesis 2 straight n minus 1 right parenthesis over denominator 6 end fraction close parentheses
end style

Answered by Sneha shidid | 13th Dec, 2017, 10:30: AM