The maths. problem is attached. Please send the complete solution step by step.

Asked by sudhanshubhushanroy | 26th Nov, 2017, 06:03: PM

Expert Answer:

begin mathsize 16px style now
straight t subscript straight r equals fraction numerator straight t over denominator 1.3.5....... left parenthesis 2 straight r plus 1 right parenthesis end fraction
straight t subscript straight r equals 1 half cross times fraction numerator 2 straight t plus 1 minus 1 over denominator 1.3.5....... left parenthesis 2 straight r minus 1 right parenthesis. left parenthesis 2 straight r plus 1 right parenthesis end fraction
2 straight t subscript straight r equals fraction numerator 1 over denominator 1.3.5....... left parenthesis 2 straight r minus 1 right parenthesis end fraction minus fraction numerator 1 over denominator 1.3.5....... left parenthesis 2 straight r plus 1 right parenthesis end fraction
2 straight t subscript 1 equals 1 minus fraction numerator 1 over denominator 1.3 end fraction
2 straight t subscript 2 equals fraction numerator 1 over denominator 1.3 end fraction minus fraction numerator 1 over denominator 1.3.5 end fraction
so
subscript straight t subscript 1 plus straight t subscript 2 plus straight t subscript 3 plus...... plus straight t subscript straight n equals 1 half open parentheses 1 minus fraction numerator 1 over denominator 1.3 end fraction plus fraction numerator 1 over denominator 1.3 end fraction minus fraction numerator 1 over denominator 1.3.5 end fraction plus......... plus fraction numerator 1 over denominator 1.3.5....... left parenthesis 2 straight n minus 1 right parenthesis end fraction minus fraction numerator 1 over denominator 1.3.5....... left parenthesis 2 straight n plus 1 right parenthesis end fraction close parentheses end subscript
so space sum equals 1 half open parentheses 1 minus fraction numerator 1 over denominator 1.3.5....... left parenthesis 2 straight n plus 1 right parenthesis end fraction close parentheses end style

Answered by Arun | 28th Nov, 2017, 04:48: PM