Find the value of : 1/(1+√2) + 1/(√2+√3)+...+1/(√2025+√2026)

Question

KnowledgeBoat · Accepted Answer

Rationalizing a general term, To rationalize, we multiply the numerator and denominator by the conjugate, : Expanding the series, First term: Second term: Third term: ... Last term: Adding all the series, Everything cancels except the first and last term. -1 + . Hence, solution = - 1.

Mathematics

Find the value of : 1/(1+√2) + 1/(√2+√3)+...+1/(√2025+√2026)

Rational Irrational Nos

Related Questions

Show that x is irrational, if :
(i) x² = 6
(ii) x² = 0.009
(iii) x² = 27

Mathematics

Find the value of : 1/(1+√2) + 1/(√2+√3)+...+1/(√2025+√2026)

Rational Irrational Nos

Related Questions

Show that x is irrational, if :(i) x2 = 6(ii) x2 = 0.009(iii) x2 = 27

Show that x is irrational, if :
(i) x² = 6
(ii) x² = 0.009
(iii) x² = 27