Question Number 208738 by Tawa11 last updated on 22/Jun/24
$$\mathrm{sum}: \\ $$$$\:\:\:\frac{\mathrm{1}}{\mathrm{1}.\mathrm{4}.\mathrm{7}}\:\:\:+\:\:\frac{\mathrm{1}}{\mathrm{4}.\mathrm{7}.\mathrm{10}}\:\:+\:\:\frac{\mathrm{1}}{\mathrm{7}.\mathrm{10}.\mathrm{13}}\:\:+\:\:\frac{\mathrm{1}}{\mathrm{10}.\mathrm{13}.\mathrm{16}}\:\:+\:\:\frac{\mathrm{1}}{\mathrm{13}.\mathrm{16}.\mathrm{19}}\:\:+\:\:…\:\:+\:\:\frac{\mathrm{1}}{\mathrm{94}.\mathrm{97}.\mathrm{100}} \\ $$
Answered by BaliramKumar last updated on 22/Jun/24
![(1/6)[(1/(1×4)) − (1/(97×100))] d= 7−1 = 10−4 = 6 (1/6)×(((97×25−1))/(97×100)) = (1/6)×((2424)/(9700)) ((404)/(9700)) = ((101)/(2425))](https://www.tinkutara.com/question/Q208752.png)
$$\frac{\mathrm{1}}{\mathrm{6}}\left[\frac{\mathrm{1}}{\mathrm{1}×\mathrm{4}}\:−\:\frac{\mathrm{1}}{\mathrm{97}×\mathrm{100}}\right]\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{d}=\:\mathrm{7}−\mathrm{1}\:=\:\mathrm{10}−\mathrm{4}\:=\:\mathrm{6} \\ $$$$\frac{\mathrm{1}}{\mathrm{6}}×\frac{\left(\mathrm{97}×\mathrm{25}−\mathrm{1}\right)}{\mathrm{97}×\mathrm{100}}\:=\:\frac{\mathrm{1}}{\mathrm{6}}×\frac{\mathrm{2424}}{\mathrm{9700}}\: \\ $$$$\:\frac{\mathrm{404}}{\mathrm{9700}}\:=\:\frac{\mathrm{101}}{\mathrm{2425}} \\ $$
Commented by Tawa11 last updated on 22/Jun/24
$$\mathrm{Thanks}\:\mathrm{sir}. \\ $$