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Grade: 11

                        

Find the sum upto n terms. 1/3 + 2/21 + 3/91 + ..........

4 years ago

Answers : (1)

Faiz
107 Points
							-> 1/1*3 + 2/3*7 + 3/7*13 ...	For eveey denom. first terms	Let a= 1+ 3 + 7...	Nth term for it will be n²-n+1	For every denom. second terms	Let b= 3 + 7 + 13....	Nth term for it will be n²+n+1	Combining we get nth term of the series	T= n / (n²-n+1)(n²+n+1)	Which can be broken as:	T= 1/2 [ 1/n²-n+1 - 1/n²+n+1]	Now put values starting from 1,2,3... And add alll..	Sum= 1/2 [ 1- 1/n²+n+1]	Sum= 1/2 ( n(n+1) / n²+n+1 )
						
4 years ago
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