Please show how to solve each problem step-by-step. Thank you!

1. Write the first 5 TERMS OF The SEQUENCE, an =( ( ) " ( 2 ) 2. Determine the convergence or divergence with the given nith term, If the sequence converges, find its limit. 2 5 ( X 2 ) 3. FIND ALL VALUES OF X FOR WHICH The SERIES CONVERGES FOR these VALUES OF X, WRITE the Sum OF the SERIES As A TEUNCTION OF X . nzo /4. CONFIRM THAT THE INTEGRAL, TEST CAN BE. APPLIED. Then USE the INTEGRAL TEST TO DETERMINE THE CONVERGENCE OR DIVERGENCE OF , THE SERIES M8 en( nti ) ntl 5. DETERMINE THE CONVERGENCE OR DIVERGENCE OF The SERIES USING ANY APPROPRIATE TEST. Z ( - 1 ) 1 3n - 2 E. 6. FIND THE INTERVAL OF CONVERGENCE OF THE POWER SERIES CHECK FOR CONVERGENCE AT ENDPOINTS OF THE INTERVAL n (- 2x )7-! n=1 nt 1 7. DETERMINE THE CONVERGENCE OR DIVERGENCE OF THE SERIES 6 - 5