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k-0-1-4k-1-1-4k-3-

Question Number 212359 by MrGaster last updated on 11/Oct/24 $$ \\ $$$$\:\:\:\:\:\:\:\:\:\underset{{k}=\mathrm{0}} {\overset{\infty} {\sum}}\left(\frac{\mathrm{1}}{\:\sqrt{\mathrm{4}{k}+\mathrm{1}}}−\frac{\mathrm{1}}{\:\sqrt{\mathrm{4}{k}+\mathrm{3}}}\right) \\ $$ Answered by MathematicalUser2357 last updated on 13/Oct/24 $$\mathrm{0}.\mathrm{622791226505}…\:… \\…

ax-2-bx-c-0-a-b-c-and-two-roots-of-the-eqn-are-5-consecutive-integers-in-some-order-Find-their-values-

Question Number 212354 by RojaTaniya last updated on 11/Oct/24 $$\:\:{ax}^{\mathrm{2}} +{bx}+{c}=\mathrm{0} \\ $$$$\:{a},{b},{c}\:{and}\:{two}\:{roots}\:{of}\:{the}\:{eqn}. \\ $$$$\:{are}\:\mathrm{5}\:{consecutive}\:{integers}\:{in}\: \\ $$$$\:{some}\:{order}.\:{Find}\:{their}\:{values}. \\ $$ Answered by Rasheed.Sindhi last updated on…

lim-k-1-n-1-k-n-ln-1-k-n-2-n-

Question Number 212335 by MrGaster last updated on 10/Oct/24 $$ \\ $$$$\underset{{n}\rightarrow\infty} {\:\:\:\:\:\:\:\:\mathrm{lim}\:\underset{{k}=\mathrm{1}} {\overset{{n}} {\sum}}\left(\mathrm{1}−\frac{{k}}{{n}}\right)\mathrm{ln}\left(\mathrm{1}+\frac{{k}}{{n}^{\mathrm{2}} }\right)} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com

Question-212341

Question Number 212341 by Spillover last updated on 10/Oct/24 Answered by Ghisom last updated on 10/Oct/24 $$\underset{\mathrm{0}} {\overset{\pi/\mathrm{4}} {\int}}\:\frac{\mathrm{sin}\:{x}\:+\mathrm{cos}\:{x}}{\mathrm{9}+\mathrm{16sin}\:\mathrm{2}{x}}{dx}= \\ $$$$\:\:\:\:\:\left[{t}=\frac{\mathrm{4}\sqrt{\mathrm{2}}}{\mathrm{5}}\mathrm{cos}\:\left({x}+\frac{\pi}{\mathrm{4}}\right)\right] \\ $$$$=−\frac{\mathrm{1}}{\mathrm{20}}\underset{\mathrm{0}} {\overset{\mathrm{4}/\mathrm{5}} {\int}}\frac{{dt}}{{t}^{\mathrm{2}}…

show-that-1-2-2-32-2-is-63-2-63-

Question Number 212325 by MASANJAJJ last updated on 10/Oct/24 $${show}\:{that}\:\mathrm{1}+\sqrt{\mathrm{2}\:}+\mathrm{2}+……….+\mathrm{32}\sqrt{\mathrm{2}\:}\:{is}\:\mathrm{63}\sqrt{\mathrm{2}}\:+\mathrm{63} \\ $$ Answered by Ghisom last updated on 10/Oct/24 $$\underset{{k}=\mathrm{0}} {\overset{{n}} {\sum}}{a}^{{k}} =\frac{{a}^{{n}+\mathrm{1}} −\mathrm{1}}{{a}−\mathrm{1}} \\…

The-number-abc-is-divisible-by-37-Prove-that-bca-cab-is-divisible-by-37-

Question Number 212342 by hardmath last updated on 10/Oct/24 $$\mathrm{The}\:\mathrm{number}\:\:\overline {\mathrm{abc}}\:\mathrm{is}\:\mathrm{divisible}\:\mathrm{by}\:\mathrm{37}. \\ $$$$\mathrm{Prove}\:\mathrm{that}\:\overline {\mathrm{bca}}\:+\:\overline {\mathrm{cab}}\:\mathrm{is}\:\mathrm{divisible}\:\mathrm{by}\:\mathrm{37}.\: \\ $$ Answered by A5T last updated on 10/Oct/24 $$\mathrm{100}{a}+\mathrm{10}{b}+{c}\equiv−\mathrm{11}{a}−\mathrm{27}{b}+{c}=−\left(\mathrm{11}{a}+\mathrm{27}{b}−{c}\right)…