Saved Bookmarks
| 1. |
The value of cot[{Sigma_(n=1)^(23){cot^(-1))1+Sigma_(k=1)^(n)2k}] is |
|
Answer» `23/25` `COT^(-1)(1+underset(k=1)overset(N)Sigma 2k)=cot^(-1)1+2underset(k=1)overset(n_Sigmak)=cot^(-1)1+n(n+1)` `=TAN^(-1)(1)/(1+n(n+1)}=(tan^(-1)(n+1)-n)/(1+n(n+1))` `tan^(-1)(n1)-tan^(-1)n` `therefore underset(n=1)overset(23)Sigma(tan^(-1)(n+1)-tan^(-1)n)` `tan^(-1)24-tan^(-1)1` `tan^(-1)(24-1)/(1+24xx1)=tan^(-1)(23)/(25)=cot^(-1)25/23` Hence `cot[underset(n=1)overset(23)Sigma{cot^(-1)(1+underset(k=1)overset(n)Sigma 2k)}]=cot^(-1)25/23=25/23` |
|